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Simplifying 8x4 + 43x2 + -5 = 0 Reorder the terms: -5 + 43x2 + 8x4 = 0 Solving -5 + 43x2 + 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'. -0.625 + 5.375x2 + x4 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 5.375x2 + 0.625 + x4 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 5.375x2 + x4 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 5.375x2 + x4 = 0 + 0.625 5.375x2 + x4 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 5.375x2 + x4 = 0.625 The x term is 5.375x2. Take half its coefficient (2.6875). Square it (7.22265625) and add it to both sides. Add '7.22265625' to each side of the equation. 5.375x2 + 7.22265625 + x4 = 0.625 + 7.22265625 Reorder the terms: 7.22265625 + 5.375x2 + x4 = 0.625 + 7.22265625 Combine like terms: 0.625 + 7.22265625 = 7.84765625 7.22265625 + 5.375x2 + x4 = 7.84765625 Factor a perfect square on the left side: (x2 + 2.6875)(x2 + 2.6875) = 7.84765625 Calculate the square root of the right side: 2.801366854 Break this problem into two subproblems by setting (x2 + 2.6875) equal to 2.801366854 and -2.801366854.Subproblem 1
x2 + 2.6875 = 2.801366854 Simplifying x2 + 2.6875 = 2.801366854 Reorder the terms: 2.6875 + x2 = 2.801366854 Solving 2.6875 + x2 = 2.801366854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6875' to each side of the equation. 2.6875 + -2.6875 + x2 = 2.801366854 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x2 = 2.801366854 + -2.6875 x2 = 2.801366854 + -2.6875 Combine like terms: 2.801366854 + -2.6875 = 0.113866854 x2 = 0.113866854 Simplifying x2 = 0.113866854 Take the square root of each side: x = {-0.337441631, 0.337441631}Subproblem 2
x2 + 2.6875 = -2.801366854 Simplifying x2 + 2.6875 = -2.801366854 Reorder the terms: 2.6875 + x2 = -2.801366854 Solving 2.6875 + x2 = -2.801366854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6875' to each side of the equation. 2.6875 + -2.6875 + x2 = -2.801366854 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x2 = -2.801366854 + -2.6875 x2 = -2.801366854 + -2.6875 Combine like terms: -2.801366854 + -2.6875 = -5.488866854 x2 = -5.488866854 Simplifying x2 = -5.488866854 Reorder the terms: 5.488866854 + x2 = -5.488866854 + 5.488866854 Combine like terms: -5.488866854 + 5.488866854 = 0.000000000 5.488866854 + 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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