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Simplifying (x2 + -4)(3x2 + -9) = 0 Reorder the terms: (-4 + x2)(3x2 + -9) = 0 Reorder the terms: (-4 + x2)(-9 + 3x2) = 0 Multiply (-4 + x2) * (-9 + 3x2) (-4(-9 + 3x2) + x2(-9 + 3x2)) = 0 ((-9 * -4 + 3x2 * -4) + x2(-9 + 3x2)) = 0 ((36 + -12x2) + x2(-9 + 3x2)) = 0 (36 + -12x2 + (-9 * x2 + 3x2 * x2)) = 0 (36 + -12x2 + (-9x2 + 3x4)) = 0 Combine like terms: -12x2 + -9x2 = -21x2 (36 + -21x2 + 3x4) = 0 Solving 36 + -21x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + -7x2 + x4) = 0 Factor a trinomial. 3((3 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. 3((3 + -1x2)((2 + x)(2 + -1x))) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -1x2 = 0 Solving 3 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x2 = 0 + -3 -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x2 = -3 Divide each side by '-1'. x2 = 3 Simplifying x2 = 3 Take the square root of each side: x = {-1.732050808, 1.732050808}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 = {-1.732050808, 1.732050808, -2, 2}
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