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Simplifying (2x2 + -3)(2x2 + -3) + -25 = 0 Reorder the terms: (-3 + 2x2)(2x2 + -3) + -25 = 0 Reorder the terms: (-3 + 2x2)(-3 + 2x2) + -25 = 0 Multiply (-3 + 2x2) * (-3 + 2x2) (-3(-3 + 2x2) + 2x2 * (-3 + 2x2)) + -25 = 0 ((-3 * -3 + 2x2 * -3) + 2x2 * (-3 + 2x2)) + -25 = 0 ((9 + -6x2) + 2x2 * (-3 + 2x2)) + -25 = 0 (9 + -6x2 + (-3 * 2x2 + 2x2 * 2x2)) + -25 = 0 (9 + -6x2 + (-6x2 + 4x4)) + -25 = 0 Combine like terms: -6x2 + -6x2 = -12x2 (9 + -12x2 + 4x4) + -25 = 0 Reorder the terms: 9 + -25 + -12x2 + 4x4 = 0 Combine like terms: 9 + -25 = -16 -16 + -12x2 + 4x4 = 0 Solving -16 + -12x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -3x2 + x4) = 0 Factor a trinomial. 4((-1 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. 4((-1 + -1x2)((2 + x)(2 + -1x))) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -1x2)' equal to zero and attempt to solve: Simplifying -1 + -1x2 = 0 Solving -1 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x2 = 0 + 1 -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x2 = 1 Divide each side by '-1'. x2 = -1 Simplifying x2 = -1 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 '(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 = {-2, 2}
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