-8(x+2)(x-12)=160

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Solution for -8(x+2)(x-12)=160 equation:


Simplifying
-8(x + 2)(x + -12) = 160

Reorder the terms:
-8(2 + x)(x + -12) = 160

Reorder the terms:
-8(2 + x)(-12 + x) = 160

Multiply (2 + x) * (-12 + x)
-8(2(-12 + x) + x(-12 + x)) = 160
-8((-12 * 2 + x * 2) + x(-12 + x)) = 160
-8((-24 + 2x) + x(-12 + x)) = 160
-8(-24 + 2x + (-12 * x + x * x)) = 160
-8(-24 + 2x + (-12x + x2)) = 160

Combine like terms: 2x + -12x = -10x
-8(-24 + -10x + x2) = 160
(-24 * -8 + -10x * -8 + x2 * -8) = 160
(192 + 80x + -8x2) = 160

Solving
192 + 80x + -8x2 = 160

Solving for variable 'x'.

Reorder the terms:
192 + -160 + 80x + -8x2 = 160 + -160

Combine like terms: 192 + -160 = 32
32 + 80x + -8x2 = 160 + -160

Combine like terms: 160 + -160 = 0
32 + 80x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + 10x + -1x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(4 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 10x + -1x2 = 0 Solving 4 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -10x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -10x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -10x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -10x + x2 = 0 + 4 -10x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -10x + x2 = 4 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 4 + 25 Reorder the terms: 25 + -10x + x2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + -10x + x2 = 29 Factor a perfect square on the left side: (x + -5)(x + -5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -5) equal to 5.385164807 and -5.385164807.

Subproblem 1

x + -5 = 5.385164807 Simplifying x + -5 = 5.385164807 Reorder the terms: -5 + x = 5.385164807 Solving -5 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.385164807 + 5 x = 5.385164807 + 5 Combine like terms: 5.385164807 + 5 = 10.385164807 x = 10.385164807 Simplifying x = 10.385164807

Subproblem 2

x + -5 = -5.385164807 Simplifying x + -5 = -5.385164807 Reorder the terms: -5 + x = -5.385164807 Solving -5 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.385164807 + 5 x = -5.385164807 + 5 Combine like terms: -5.385164807 + 5 = -0.385164807 x = -0.385164807 Simplifying x = -0.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.385164807, -0.385164807}

Solution

x = {10.385164807, -0.385164807}

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