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Simplifying (x2 + -4)(x2 + -10) = 72 Reorder the terms: (-4 + x2)(x2 + -10) = 72 Reorder the terms: (-4 + x2)(-10 + x2) = 72 Multiply (-4 + x2) * (-10 + x2) (-4(-10 + x2) + x2(-10 + x2)) = 72 ((-10 * -4 + x2 * -4) + x2(-10 + x2)) = 72 ((40 + -4x2) + x2(-10 + x2)) = 72 (40 + -4x2 + (-10 * x2 + x2 * x2)) = 72 (40 + -4x2 + (-10x2 + x4)) = 72 Combine like terms: -4x2 + -10x2 = -14x2 (40 + -14x2 + x4) = 72 Solving 40 + -14x2 + x4 = 72 Solving for variable 'x'. Reorder the terms: 40 + -72 + -14x2 + x4 = 72 + -72 Combine like terms: 40 + -72 = -32 -32 + -14x2 + x4 = 72 + -72 Combine like terms: 72 + -72 = 0 -32 + -14x2 + x4 = 0 Factor a trinomial. (-2 + -1x2)(16 + -1x2) = 0 Factor a difference between two squares. (-2 + -1x2)((4 + x)(4 + -1x)) = 0Subproblem 1
Set the factor '(-2 + -1x2)' equal to zero and attempt to solve: Simplifying -2 + -1x2 = 0 Solving -2 + -1x2 = 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 + -1x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x2 = 0 + 2 -1x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1x2 = 2 Divide each side by '-1'. x2 = -2 Simplifying x2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4, 4}
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