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Why quadratic equation is called quadratic?
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is Where x represents a variable, and a, b, and c, constants, with a ≠ 0. (If a = 0, the equation becomes a linear equation.) The constants a, b, and c, are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. The term "quadratic" comes from quadratus, which is the Latin word for "square." Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula (given below). One common use of quadratic equations is computing trajectories in projectile motion. Because it is in the form of ax^2+bx+c=0
What is completing the square used for?
Completing the square is a method used to solve a quadratic function. This is a handy method when there are two instances of the same variable in the function.
What are at least four ways in how to solve a quadratic equation?
1 By factorizing it 2 By sketching it on the Cartesian plane 3 By finding the difference of two squares 4 By completing the square 5 By using the quadratic equation formula 6 By finding its discriminant to see if it has any solutions at all
Which the easy way the method of factoring or the solving the quadratic equation?
By knowing how to use the quadratic equation formula.
How can you use substitution method to solve a system of equations that does not have a variable with a coefficient of 1 or -1?
2
Completing the square method?
2x² - 4x +3 = 2(x² - 2x) + 3 = 2(x² - 2x + (2/2)²) + 3 - [2*(2/2)²] (you add (2/2)² in equation. you need to subtract same amount [2*(2/2)²] in equation.) = 2(x² - 2x + 1) + 3 - 2 = 2(x² - 2x + 1) + 1 = 2(x -1)² + 1 if you are still confused, I want you to follow the related link that explains the concept of completing the square clearly.
Why does the method completing the square fit the equation 4x2-8x-5 equals 0?
Completing the square is a method used to solve quadratic equations by rewriting the equation in the form ( (x - p)^2 = q ). For the equation ( 4x^2 - 8x - 5 = 0 ), we first factor out 4 from the quadratic terms to get ( 4(x^2 - 2x) - 5 = 0 ). Then, we complete the square for ( x^2 - 2x ) by adding and subtracting 1, leading to ( 4((x - 1)^2 - 1) - 5 = 0 ). This allows us to solve for ( x ) easily by isolating the squared term.
What is the third step in solving this equation by completing the square?
Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by several methods including factoring, graphing, using the square roots or the quadratic formula. Completing the square will always work when solving quadratic equations and is a good tool to have. Solving a quadratic equation by completing the square is used in a lot of word problems.I want you to follow the related link that explains the concept of completing the square clearly and gives some examples. that video is from brightstorm.
What is the first step in solving a quadratic equation by using the squared root method?
get a life and hobbies then this question wont even be relevent
Why is the completing the square method call completing the square?
The method is called "completing the square" because it involves rearranging a quadratic equation into a perfect square trinomial. This process allows us to express the quadratic in the form ((x - p)^2 = q), where (p) and (q) are constants. By completing the square, we can easily solve for the variable and analyze the properties of the quadratic function, such as its vertex.
How does the method for solving equations with fractional or decimal coefficient and constants with the method for solving equation a with integer coeffients and constants?
Fractional u multiply and decimal u multiply and integers u minuse or add them
Why quadratic equation is called quadratic?
In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is Where x represents a variable, and a, b, and c, constants, with a ≠ 0. (If a = 0, the equation becomes a linear equation.) The constants a, b, and c, are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. The term "quadratic" comes from quadratus, which is the Latin word for "square." Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula (given below). One common use of quadratic equations is computing trajectories in projectile motion. Because it is in the form of ax^2+bx+c=0
What is the centre of a circle and its radius on the Cartesian plane whose equation is x squared plus y squared equals 12x -10y -12 showing key aspects of work?
Equation of the circle is: x2 + y2 = 12x - 10y - 12 which can written as: x2 - 12x + y2 + 10y = -12 Now by the method of completing square we can get the coordinates of the center of the circle: Coefficient of x2 = 1 Coefficient of x = -12 = -2(6) So -12x can be written as -2(x)(6) ...(1) It is clear that by adding suitable term we obtain (a - b)2 or (a + b)2 The term -2ab is in the expansion of (a - b)2 so: From 1 it is clear that b is 6. So we need to add 62 to both sides of the equation. Coefficient of y2 = 1 Coefficient of y = 10 = 2(5) So 10y can be written as 2(y)(5) ...(2) The term 2ab is in the expansion of (a + b)2 so: From 2 it is clear that b is 5. So we need to add 52 to both sides of the equation. The equation of circle, now, becomes: x2 - 12x + 62 + y2 + 10y + 52 = -12 + 62 + 52 (x - 6)2 + (y + 5)2 = 49 (x - 6)2 + (y + 5)2 = 72 (x - 6)2 + (y - (-5))2 = 72 So the coordinates of the center is 6,-5 and its radius is 7 units.
How do you complete the square x squared plus 12x plus?
36.1. You take the coefficient of x : = 122. Halve it : = 63. Then square it : = 364. Add it.This gives x2 + 12x + 36 = (x + 6)2The above method only works if the coefficient of x2 is 1. If it is not then the processs is slightly more complicated.
Can all quadratics be solved by completing the square?
Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by factoring, using the square roots or quadratic formula. Solving quadratic equations by completing the square will always work when solving quadratic equations-You can also use division or even simply take a GCF, set the quantities( ) equal to zero, and subtract or add to solve for the variable
What makes a completing square a good method?
Completing the square is a valuable method for solving quadratic equations because it transforms the equation into a form that makes it easy to identify the vertex of the parabola, allowing for straightforward graphing and analysis. It also facilitates finding the roots of the equation and can simplify integration in calculus. Additionally, this technique highlights the relationship between the coefficients of the quadratic and the geometry of the parabola. Overall, it provides a deeper understanding of quadratic functions and their properties.
What are the methods how to solve quadratic equation?
Quadratic equations can be solved using several methods: Factoring: Finding two numbers that multiply to the constant term and add to the coefficient of the linear term, allowing the equation to be expressed as a product of binomials. Completing the Square: Rearranging the equation so that one side forms a perfect square trinomial, then solving for the variable. Quadratic Formula: Using the formula ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), where ( ax^2 + bx + c = 0 ), to find the roots directly. Each method has its advantages depending on the specific equation.
