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Simplifying (4x2 + -3)(4x2 + 3) = 0 Reorder the terms: (-3 + 4x2)(4x2 + 3) = 0 Reorder the terms: (-3 + 4x2)(3 + 4x2) = 0 Multiply (-3 + 4x2) * (3 + 4x2) (-3(3 + 4x2) + 4x2 * (3 + 4x2)) = 0 ((3 * -3 + 4x2 * -3) + 4x2 * (3 + 4x2)) = 0 ((-9 + -12x2) + 4x2 * (3 + 4x2)) = 0 (-9 + -12x2 + (3 * 4x2 + 4x2 * 4x2)) = 0 (-9 + -12x2 + (12x2 + 16x4)) = 0 Combine like terms: -12x2 + 12x2 = 0 (-9 + 0 + 16x4) = 0 (-9 + 16x4) = 0 Solving -9 + 16x4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 16x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 16x4 = 0 + 9 16x4 = 0 + 9 Combine like terms: 0 + 9 = 9 16x4 = 9 Divide each side by '16'. x4 = 0.5625 Simplifying x4 = 0.5625 Reorder the terms: -0.5625 + x4 = 0.5625 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 -0.5625 + x4 = 0.0000 Factor a difference between two squares. (0.75 + x2)(-0.75 + x2) = 0.0000Subproblem 1
Set the factor '(0.75 + x2)' equal to zero and attempt to solve: Simplifying 0.75 + x2 = 0 Solving 0.75 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = 0 + -0.75 x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 x2 = -0.75 Simplifying x2 = -0.75 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 '(-0.75 + x2)' equal to zero and attempt to solve: Simplifying -0.75 + x2 = 0 Solving -0.75 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x2 = 0 + 0.75 x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 x2 = 0.75 Simplifying x2 = 0.75 Take the square root of each side: x = {-0.866025404, 0.866025404}Solution
x = {-0.866025404, 0.866025404}
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