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Simplifying 0 = 2x4 + -16x2 + -91 Reorder the terms: 0 = -91 + -16x2 + 2x4 Solving 0 = -91 + -16x2 + 2x4 Solving for variable 'x'. Combine like terms: 0 + 91 = 91 91 + 16x2 + -2x4 = -91 + -16x2 + 2x4 + 91 + 16x2 + -2x4 Reorder the terms: 91 + 16x2 + -2x4 = -91 + 91 + -16x2 + 16x2 + 2x4 + -2x4 Combine like terms: -91 + 91 = 0 91 + 16x2 + -2x4 = 0 + -16x2 + 16x2 + 2x4 + -2x4 91 + 16x2 + -2x4 = -16x2 + 16x2 + 2x4 + -2x4 Combine like terms: -16x2 + 16x2 = 0 91 + 16x2 + -2x4 = 0 + 2x4 + -2x4 91 + 16x2 + -2x4 = 2x4 + -2x4 Combine like terms: 2x4 + -2x4 = 0 91 + 16x2 + -2x4 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -45.5 + -8x2 + x4 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + -8x2 + 45.5 + x4 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + -8x2 + x4 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + -8x2 + x4 = 0 + 45.5 -8x2 + x4 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 -8x2 + x4 = 45.5 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = 45.5 + 16 Reorder the terms: 16 + -8x2 + x4 = 45.5 + 16 Combine like terms: 45.5 + 16 = 61.5 16 + -8x2 + x4 = 61.5 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 61.5 Calculate the square root of the right side: 7.842193571 Break this problem into two subproblems by setting (x2 + -4) equal to 7.842193571 and -7.842193571.Subproblem 1
x2 + -4 = 7.842193571 Simplifying x2 + -4 = 7.842193571 Reorder the terms: -4 + x2 = 7.842193571 Solving -4 + x2 = 7.842193571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 7.842193571 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 7.842193571 + 4 x2 = 7.842193571 + 4 Combine like terms: 7.842193571 + 4 = 11.842193571 x2 = 11.842193571 Simplifying x2 = 11.842193571 Take the square root of each side: x = {-3.441248839, 3.441248839}Subproblem 2
x2 + -4 = -7.842193571 Simplifying x2 + -4 = -7.842193571 Reorder the terms: -4 + x2 = -7.842193571 Solving -4 + x2 = -7.842193571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -7.842193571 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -7.842193571 + 4 x2 = -7.842193571 + 4 Combine like terms: -7.842193571 + 4 = -3.842193571 x2 = -3.842193571 Simplifying x2 = -3.842193571 Reorder the terms: 3.842193571 + x2 = -3.842193571 + 3.842193571 Combine like terms: -3.842193571 + 3.842193571 = 0.000000000 3.842193571 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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