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Simplifying 4x2(x2 + 1) + -9(x2 + 1) = 0 Reorder the terms: 4x2(1 + x2) + -9(x2 + 1) = 0 (1 * 4x2 + x2 * 4x2) + -9(x2 + 1) = 0 (4x2 + 4x4) + -9(x2 + 1) = 0 Reorder the terms: 4x2 + 4x4 + -9(1 + x2) = 0 4x2 + 4x4 + (1 * -9 + x2 * -9) = 0 4x2 + 4x4 + (-9 + -9x2) = 0 Reorder the terms: -9 + 4x2 + -9x2 + 4x4 = 0 Combine like terms: 4x2 + -9x2 = -5x2 -9 + -5x2 + 4x4 = 0 Solving -9 + -5x2 + 4x4 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x2)(9 + -4x2) = 0 Factor a difference between two squares. (-1 + -1x2)((3 + 2x)(3 + -2x)) = 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-1.5, 1.5}
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