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Simplifying (8 + -2x4)(8 + -2x4) = 0 Multiply (8 + -2x4) * (8 + -2x4) (8(8 + -2x4) + -2x4 * (8 + -2x4)) = 0 ((8 * 8 + -2x4 * 8) + -2x4 * (8 + -2x4)) = 0 ((64 + -16x4) + -2x4 * (8 + -2x4)) = 0 (64 + -16x4 + (8 * -2x4 + -2x4 * -2x4)) = 0 (64 + -16x4 + (-16x4 + 4x8)) = 0 Combine like terms: -16x4 + -16x4 = -32x4 (64 + -32x4 + 4x8) = 0 Solving 64 + -32x4 + 4x8 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + -8x4 + x8) = 0 Factor a trinomial. 4((4 + -1x4)(4 + -1x4)) = 0 Factor a difference between two squares. 4(((2 + x2)(2 + -1x2))(4 + -1x4)) = 0 Factor a difference between two squares. 4(((2 + x2)(2 + -1x2))(2 + x2)(2 + -1x2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + x2)' equal to zero and attempt to solve: Simplifying 2 + x2 = 0 Solving 2 + x2 = 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 + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 0 + -2 x2 = 0 + -2 Combine like terms: 0 + -2 = -2 x2 = -2 Simplifying x2 = -2 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 '(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 3
Set the factor '(2 + x2)' equal to zero and attempt to solve: Simplifying 2 + x2 = 0 Solving 2 + x2 = 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 + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 0 + -2 x2 = 0 + -2 Combine like terms: 0 + -2 = -2 x2 = -2 Simplifying x2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
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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