(x+6)*(x-8)=676

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Solution for (x+6)*(x-8)=676 equation:


Simplifying
(x + 6)(x + -8) = 676

Reorder the terms:
(6 + x)(x + -8) = 676

Reorder the terms:
(6 + x)(-8 + x) = 676

Multiply (6 + x) * (-8 + x)
(6(-8 + x) + x(-8 + x)) = 676
((-8 * 6 + x * 6) + x(-8 + x)) = 676
((-48 + 6x) + x(-8 + x)) = 676
(-48 + 6x + (-8 * x + x * x)) = 676
(-48 + 6x + (-8x + x2)) = 676

Combine like terms: 6x + -8x = -2x
(-48 + -2x + x2) = 676

Solving
-48 + -2x + x2 = 676

Solving for variable 'x'.

Reorder the terms:
-48 + -676 + -2x + x2 = 676 + -676

Combine like terms: -48 + -676 = -724
-724 + -2x + x2 = 676 + -676

Combine like terms: 676 + -676 = 0
-724 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '724' to each side of the equation.
-724 + -2x + 724 + x2 = 0 + 724

Reorder the terms:
-724 + 724 + -2x + x2 = 0 + 724

Combine like terms: -724 + 724 = 0
0 + -2x + x2 = 0 + 724
-2x + x2 = 0 + 724

Combine like terms: 0 + 724 = 724
-2x + x2 = 724

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 724 + 1

Reorder the terms:
1 + -2x + x2 = 724 + 1

Combine like terms: 724 + 1 = 725
1 + -2x + x2 = 725

Factor a perfect square on the left side:
(x + -1)(x + -1) = 725

Calculate the square root of the right side: 26.925824036

Break this problem into two subproblems by setting 
(x + -1) equal to 26.925824036 and -26.925824036.

Subproblem 1

x + -1 = 26.925824036 Simplifying x + -1 = 26.925824036 Reorder the terms: -1 + x = 26.925824036 Solving -1 + x = 26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 26.925824036 + 1 Combine like terms: -1 + 1 = 0 0 + x = 26.925824036 + 1 x = 26.925824036 + 1 Combine like terms: 26.925824036 + 1 = 27.925824036 x = 27.925824036 Simplifying x = 27.925824036

Subproblem 2

x + -1 = -26.925824036 Simplifying x + -1 = -26.925824036 Reorder the terms: -1 + x = -26.925824036 Solving -1 + x = -26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -26.925824036 + 1 Combine like terms: -1 + 1 = 0 0 + x = -26.925824036 + 1 x = -26.925824036 + 1 Combine like terms: -26.925824036 + 1 = -25.925824036 x = -25.925824036 Simplifying x = -25.925824036

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.925824036, -25.925824036}

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