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Simplifying (x2 + 1)(x2 + -25) = 0 Reorder the terms: (1 + x2)(x2 + -25) = 0 Reorder the terms: (1 + x2)(-25 + x2) = 0 Multiply (1 + x2) * (-25 + x2) (1(-25 + x2) + x2(-25 + x2)) = 0 ((-25 * 1 + x2 * 1) + x2(-25 + x2)) = 0 ((-25 + 1x2) + x2(-25 + x2)) = 0 (-25 + 1x2 + (-25 * x2 + x2 * x2)) = 0 (-25 + 1x2 + (-25x2 + x4)) = 0 Combine like terms: 1x2 + -25x2 = -24x2 (-25 + -24x2 + x4) = 0 Solving -25 + -24x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x2)(25 + -1x2) = 0 Factor a difference between two squares. (-1 + -1x2)((5 + x)(5 + -1x)) = 0Subproblem 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-5, 5}
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