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Simplifying (x2 + 13)(x2 + 1) = 85 Reorder the terms: (13 + x2)(x2 + 1) = 85 Reorder the terms: (13 + x2)(1 + x2) = 85 Multiply (13 + x2) * (1 + x2) (13(1 + x2) + x2(1 + x2)) = 85 ((1 * 13 + x2 * 13) + x2(1 + x2)) = 85 ((13 + 13x2) + x2(1 + x2)) = 85 (13 + 13x2 + (1 * x2 + x2 * x2)) = 85 (13 + 13x2 + (1x2 + x4)) = 85 Combine like terms: 13x2 + 1x2 = 14x2 (13 + 14x2 + x4) = 85 Solving 13 + 14x2 + x4 = 85 Solving for variable 'x'. Reorder the terms: 13 + -85 + 14x2 + x4 = 85 + -85 Combine like terms: 13 + -85 = -72 -72 + 14x2 + x4 = 85 + -85 Combine like terms: 85 + -85 = 0 -72 + 14x2 + x4 = 0 Factor a trinomial. (-18 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. (-18 + -1x2)((2 + x)(2 + -1x)) = 0Subproblem 1
Set the factor '(-18 + -1x2)' equal to zero and attempt to solve: Simplifying -18 + -1x2 = 0 Solving -18 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1x2 = 0 + 18 -1x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1x2 = 18 Divide each side by '-1'. x2 = -18 Simplifying x2 = -18 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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