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Simplifying 6x4 + -19x2 + 7 = 2x4 + -5 Reorder the terms: 7 + -19x2 + 6x4 = 2x4 + -5 Reorder the terms: 7 + -19x2 + 6x4 = -5 + 2x4 Solving 7 + -19x2 + 6x4 = -5 + 2x4 Solving for variable 'x'. Reorder the terms: 7 + 5 + -19x2 + 6x4 + -2x4 = -5 + 2x4 + 5 + -2x4 Combine like terms: 7 + 5 = 12 12 + -19x2 + 6x4 + -2x4 = -5 + 2x4 + 5 + -2x4 Combine like terms: 6x4 + -2x4 = 4x4 12 + -19x2 + 4x4 = -5 + 2x4 + 5 + -2x4 Reorder the terms: 12 + -19x2 + 4x4 = -5 + 5 + 2x4 + -2x4 Combine like terms: -5 + 5 = 0 12 + -19x2 + 4x4 = 0 + 2x4 + -2x4 12 + -19x2 + 4x4 = 2x4 + -2x4 Combine like terms: 2x4 + -2x4 = 0 12 + -19x2 + 4x4 = 0 Factor a trinomial. (3 + -4x2)(4 + -1x2) = 0 Factor a difference between two squares. (3 + -4x2)((2 + x)(2 + -1x)) = 0Subproblem 1
Set the factor '(3 + -4x2)' equal to zero and attempt to solve: Simplifying 3 + -4x2 = 0 Solving 3 + -4x2 = 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 + -4x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x2 = 0 + -3 -4x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4x2 = -3 Divide each side by '-4'. x2 = 0.75 Simplifying x2 = 0.75 Take the square root of each side: x = {-0.866025404, 0.866025404}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 = {-0.866025404, 0.866025404, -2, 2}
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