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.
The method of completing the square has its roots in ancient mathematics, but it was notably developed and formalized by mathematicians during the Islamic Golden Age, particularly by Al-Khwarizmi in the 9th century. His work on quadratic equations laid the foundation for this technique. The method later influenced European mathematicians during the Renaissance, further solidifying its importance in algebra.
The first step, in solving a quadratic equation in a variable x using this method, is to complete the square defined by the terms in x2 and x, by adding and subtracting a suitable constant.
If you aren't dealing with algebra, such as x2+3x+21, then completing the square wont be able to solve the porblem, however if you are using algebra, and you cannot factorise, then completing the square will always work
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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.
i want to solve few questions of completing square method can u give me some questions on it
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.
The method of completing the square has its roots in ancient mathematics, but it was notably developed and formalized by mathematicians during the Islamic Golden Age, particularly by Al-Khwarizmi in the 9th century. His work on quadratic equations laid the foundation for this technique. The method later influenced European mathematicians during the Renaissance, further solidifying its importance in algebra.
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
Divide all terms by 3 so:- x2-4x = 5 Completing the square:- (x-2)2 = 9 x-2 = -/+3 x = -1 or x = 5
The first step, in solving a quadratic equation in a variable x using this method, is to complete the square defined by the terms in x2 and x, by adding and subtracting a suitable constant.
Completing the square would be the same as "Finding the square root" So an example would be 16. 16 is a perfect square so it would reduce to 4.
If you aren't dealing with algebra, such as x2+3x+21, then completing the square wont be able to solve the porblem, however if you are using algebra, and you cannot factorise, then completing the square will always work
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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.
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.