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Simplifying (x2 + 5)(x2 + 5) + -15(x2 + 5) + 54 = 0 Reorder the terms: (5 + x2)(x2 + 5) + -15(x2 + 5) + 54 = 0 Reorder the terms: (5 + x2)(5 + x2) + -15(x2 + 5) + 54 = 0 Multiply (5 + x2) * (5 + x2) (5(5 + x2) + x2(5 + x2)) + -15(x2 + 5) + 54 = 0 ((5 * 5 + x2 * 5) + x2(5 + x2)) + -15(x2 + 5) + 54 = 0 ((25 + 5x2) + x2(5 + x2)) + -15(x2 + 5) + 54 = 0 (25 + 5x2 + (5 * x2 + x2 * x2)) + -15(x2 + 5) + 54 = 0 (25 + 5x2 + (5x2 + x4)) + -15(x2 + 5) + 54 = 0 Combine like terms: 5x2 + 5x2 = 10x2 (25 + 10x2 + x4) + -15(x2 + 5) + 54 = 0 Reorder the terms: 25 + 10x2 + x4 + -15(5 + x2) + 54 = 0 25 + 10x2 + x4 + (5 * -15 + x2 * -15) + 54 = 0 25 + 10x2 + x4 + (-75 + -15x2) + 54 = 0 Reorder the terms: 25 + -75 + 54 + 10x2 + -15x2 + x4 = 0 Combine like terms: 25 + -75 = -50 -50 + 54 + 10x2 + -15x2 + x4 = 0 Combine like terms: -50 + 54 = 4 4 + 10x2 + -15x2 + x4 = 0 Combine like terms: 10x2 + -15x2 = -5x2 4 + -5x2 + x4 = 0 Solving 4 + -5x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(4 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(1 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 3
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 4
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, 1, -2, 2}
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