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Simplifying 1 + 2x4 = x2(x2 + 3) + x2 + -3 Reorder the terms: 1 + 2x4 = x2(3 + x2) + x2 + -3 1 + 2x4 = (3 * x2 + x2 * x2) + x2 + -3 1 + 2x4 = (3x2 + x4) + x2 + -3 Reorder the terms: 1 + 2x4 = -3 + 3x2 + x2 + x4 Combine like terms: 3x2 + x2 = 4x2 1 + 2x4 = -3 + 4x2 + x4 Solving 1 + 2x4 = -3 + 4x2 + x4 Solving for variable 'x'. Reorder the terms: 1 + 3 + -4x2 + 2x4 + -1x4 = -3 + 4x2 + x4 + 3 + -4x2 + -1x4 Combine like terms: 1 + 3 = 4 4 + -4x2 + 2x4 + -1x4 = -3 + 4x2 + x4 + 3 + -4x2 + -1x4 Combine like terms: 2x4 + -1x4 = 1x4 4 + -4x2 + 1x4 = -3 + 4x2 + x4 + 3 + -4x2 + -1x4 Reorder the terms: 4 + -4x2 + 1x4 = -3 + 3 + 4x2 + -4x2 + x4 + -1x4 Combine like terms: -3 + 3 = 0 4 + -4x2 + 1x4 = 0 + 4x2 + -4x2 + x4 + -1x4 4 + -4x2 + 1x4 = 4x2 + -4x2 + x4 + -1x4 Combine like terms: 4x2 + -4x2 = 0 4 + -4x2 + 1x4 = 0 + x4 + -1x4 4 + -4x2 + 1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 4 + -4x2 + 1x4 = 0 Factor a trinomial. (2 + -1x2)(2 + -1x2) = 0Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 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 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 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 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Solution
x = {-1.414213562, 1.414213562, -1.414213562, 1.414213562}
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