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Simplifying 9x4 + 4x2 + 5 = 15x2 + 3 Reorder the terms: 5 + 4x2 + 9x4 = 15x2 + 3 Reorder the terms: 5 + 4x2 + 9x4 = 3 + 15x2 Solving 5 + 4x2 + 9x4 = 3 + 15x2 Solving for variable 'x'. Reorder the terms: 5 + -3 + 4x2 + -15x2 + 9x4 = 3 + 15x2 + -3 + -15x2 Combine like terms: 5 + -3 = 2 2 + 4x2 + -15x2 + 9x4 = 3 + 15x2 + -3 + -15x2 Combine like terms: 4x2 + -15x2 = -11x2 2 + -11x2 + 9x4 = 3 + 15x2 + -3 + -15x2 Reorder the terms: 2 + -11x2 + 9x4 = 3 + -3 + 15x2 + -15x2 Combine like terms: 3 + -3 = 0 2 + -11x2 + 9x4 = 0 + 15x2 + -15x2 2 + -11x2 + 9x4 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 2 + -11x2 + 9x4 = 0 Factor a trinomial. (2 + -9x2)(1 + -1x2) = 0 Factor a difference between two squares. (2 + -9x2)((1 + x)(1 + -1x)) = 0Subproblem 1
Set the factor '(2 + -9x2)' equal to zero and attempt to solve: Simplifying 2 + -9x2 = 0 Solving 2 + -9x2 = 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 + -9x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9x2 = 0 + -2 -9x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -9x2 = -2 Divide each side by '-9'. x2 = 0.2222222222 Simplifying x2 = 0.2222222222 Take the square root of each side: x = {-0.471404521, 0.471404521}Subproblem 2
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 3
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 = 1Solution
x = {-0.471404521, 0.471404521, -1, 1}
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