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Examplex2 + 3x = 8x - 6
Step 1The first step is to move all terms to the left using addition and subtraction. First, we will subtract 8x from each side.x2 + 3x - 8x = 8x - 8x - 6x2 - 5x = -6
Now, we will add 6 to each side.x2 - 5x + 6 = -6 + 6
x2 - 5x + 6 = 0.
With all terms on the left side, we proceed to Step 2.
Step 2We identify the left as a trinomial, and factor it accordingly:(x - 2)(x - 3) = 0We now have two factors, (x - 2) and (x - 3).
Step 3We now set each factor equal to zero. The result is two subproblems:x - 2 = 0andx - 3 = 0
Solving the first subproblem, x - 2 = 0, gives x = 2. Solving the second subproblem, x - 3 = 0, gives x = 3.
Step 4The final step is to combine the two previous solutions, x = 2 and x = 3, into one solution for the original problem.x2 + 3x = 8x - 6x = 2, 3
What else can I help you with?
Factoring a linear equation?
Factoring a linear equation typically involves expressing it in the form (y = mx + b) as a product of its components. However, linear equations are generally not factored like polynomials since they represent straight lines. Instead, you can rearrange or rewrite them to isolate variables or simplify expressions, but true factoring applies more to quadratic or higher-degree polynomials. For example, the equation (2x + 4 = 0) can be rewritten as (2(x + 2) = 0), showcasing a basic factorization approach.
What part of the a quadratic formula tells you when the quadratic equation can be solved by factoring?
The discriminant
When is it easier to solve a quadratic equation by factoring than to solve it using a table?
It is easier to solve a quadratic equation by factoring when the equation can be expressed as a product of two binomials that easily yield integer roots. This method is often quicker for simpler quadratics with small coefficients. In contrast, using a table to find solutions can be more cumbersome and time-consuming, particularly for equations where the roots are not integers or when the quadratic is more complex. Thus, factoring is preferred when the equation allows for straightforward factorization.
What is an equation with an exponent of 2?
An equation with an exponent of 2 is a quadratic equation, which typically takes the form ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are constants and ( a \neq 0 ). An example of such an equation is ( 2x^2 - 4x + 1 = 0 ). Quadratic equations can be solved using methods like factoring, completing the square, or the quadratic formula.
How do you solve 4x2 minus 30x plus 45 by factoring?
The discriminant for the quadratic is b2-4ac = 302 - 4*4*45 = 900 - 720 = 180 Since 180 is not a perfect square, the roots of the equation are irrational and it is far from straightforward to solve such an equation by factoring.
What equation results from completing the square and then factoring?
A quadratic equation
What is an equation that can be used in quadratic formula completing the square and factoring?
A quadratic equation.
Why is factoring important?
It makes a complex equation more manipuable.
Which the easy way the method of factoring or the solving the quadratic equation?
By knowing how to use the quadratic equation formula.
Factoring a linear equation?
Factoring a linear equation typically involves expressing it in the form (y = mx + b) as a product of its components. However, linear equations are generally not factored like polynomials since they represent straight lines. Instead, you can rearrange or rewrite them to isolate variables or simplify expressions, but true factoring applies more to quadratic or higher-degree polynomials. For example, the equation (2x + 4 = 0) can be rewritten as (2(x + 2) = 0), showcasing a basic factorization approach.
What part of the a quadratic formula tells you when the quadratic equation can be solved by factoring?
The discriminant
What is the definition of quadratic equation of factoring?
its easy first,xczxczxczxczxc....ERROR..vxbdxv
When is it easier to solve a quadratic equation by factoring than to solve it using a table?
It is easier to solve a quadratic equation by factoring when the equation can be expressed as a product of two binomials that easily yield integer roots. This method is often quicker for simpler quadratics with small coefficients. In contrast, using a table to find solutions can be more cumbersome and time-consuming, particularly for equations where the roots are not integers or when the quadratic is more complex. Thus, factoring is preferred when the equation allows for straightforward factorization.
What equation results from completing the square and then factoring x2-8x39?
(X-4)^2=55
What is an equation with an exponent of 2?
An equation with an exponent of 2 is a quadratic equation, which typically takes the form ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are constants and ( a \neq 0 ). An example of such an equation is ( 2x^2 - 4x + 1 = 0 ). Quadratic equations can be solved using methods like factoring, completing the square, or the quadratic formula.
What is the step-by-step procedure for solving a quadratic equation using the keyword "factoring"?
To solve a quadratic equation using factoring, follow these steps: Write the equation in the form ax2 bx c 0. Factor the quadratic expression on the left side of the equation. Set each factor equal to zero and solve for x. Check the solutions by substituting them back into the original equation. The solutions are the values of x that make the equation true.
How do you solve 4x2 minus 30x plus 45 by factoring?
The discriminant for the quadratic is b2-4ac = 302 - 4*4*45 = 900 - 720 = 180 Since 180 is not a perfect square, the roots of the equation are irrational and it is far from straightforward to solve such an equation by factoring.
