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Simplifying 8x4 + 7x2 + -13 = 0 Reorder the terms: -13 + 7x2 + 8x4 = 0 Solving -13 + 7x2 + 8x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + 0.875x2 + x4 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 0.875x2 + 1.625 + x4 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 0.875x2 + x4 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 0.875x2 + x4 = 0 + 1.625 0.875x2 + x4 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 0.875x2 + x4 = 1.625 The x term is 0.875x2. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x2 + 0.19140625 + x4 = 1.625 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x2 + x4 = 1.625 + 0.19140625 Combine like terms: 1.625 + 0.19140625 = 1.81640625 0.19140625 + 0.875x2 + x4 = 1.81640625 Factor a perfect square on the left side: (x2 + 0.4375)(x2 + 0.4375) = 1.81640625 Calculate the square root of the right side: 1.347741166 Break this problem into two subproblems by setting (x2 + 0.4375) equal to 1.347741166 and -1.347741166.Subproblem 1
x2 + 0.4375 = 1.347741166 Simplifying x2 + 0.4375 = 1.347741166 Reorder the terms: 0.4375 + x2 = 1.347741166 Solving 0.4375 + x2 = 1.347741166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x2 = 1.347741166 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x2 = 1.347741166 + -0.4375 x2 = 1.347741166 + -0.4375 Combine like terms: 1.347741166 + -0.4375 = 0.910241166 x2 = 0.910241166 Simplifying x2 = 0.910241166 Take the square root of each side: x = {-0.954065598, 0.954065598}Subproblem 2
x2 + 0.4375 = -1.347741166 Simplifying x2 + 0.4375 = -1.347741166 Reorder the terms: 0.4375 + x2 = -1.347741166 Solving 0.4375 + x2 = -1.347741166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x2 = -1.347741166 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x2 = -1.347741166 + -0.4375 x2 = -1.347741166 + -0.4375 Combine like terms: -1.347741166 + -0.4375 = -1.785241166 x2 = -1.785241166 Simplifying x2 = -1.785241166 Reorder the terms: 1.785241166 + x2 = -1.785241166 + 1.785241166 Combine like terms: -1.785241166 + 1.785241166 = 0.000000000 1.785241166 + 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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