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Simplifying -4(x2 + -12) = x2(12 + -1x2) Reorder the terms: -4(-12 + x2) = x2(12 + -1x2) (-12 * -4 + x2 * -4) = x2(12 + -1x2) (48 + -4x2) = x2(12 + -1x2) 48 + -4x2 = (12 * x2 + -1x2 * x2) 48 + -4x2 = (12x2 + -1x4) Solving 48 + -4x2 = 12x2 + -1x4 Solving for variable 'x'. Combine like terms: -4x2 + -12x2 = -16x2 48 + -16x2 + x4 = 12x2 + -1x4 + -12x2 + x4 Reorder the terms: 48 + -16x2 + x4 = 12x2 + -12x2 + -1x4 + x4 Combine like terms: 12x2 + -12x2 = 0 48 + -16x2 + x4 = 0 + -1x4 + x4 48 + -16x2 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 48 + -16x2 + x4 = 0 Factor a trinomial. (4 + -1x2)(12 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(12 + -1x2) = 0Subproblem 1
Set the factor '(12 + -1x2)' equal to zero and attempt to solve: Simplifying 12 + -1x2 = 0 Solving 12 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x2 = 0 + -12 -1x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -1x2 = -12 Divide each side by '-1'. x2 = 12 Simplifying x2 = 12 Take the square root of each side: x = {-3.464101615, 3.464101615}Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-3.464101615, 3.464101615, -2, 2}
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