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Simplifying x2 + -18x4 + 32 = 0 Reorder the terms: 32 + x2 + -18x4 = 0 Solving 32 + x2 + -18x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -1.777777778 + -0.05555555556x2 + x4 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.05555555556x2 + 1.777777778 + x4 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.05555555556x2 + x4 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.05555555556x2 + x4 = 0 + 1.777777778 -0.05555555556x2 + x4 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.05555555556x2 + x4 = 1.777777778 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.05555555556x2 + 0.25 + x4 = 1.777777778 + 0.25 Reorder the terms: 0.25 + -0.05555555556x2 + x4 = 1.777777778 + 0.25 Combine like terms: 1.777777778 + 0.25 = 2.027777778 0.25 + -0.05555555556x2 + x4 = 2.027777778 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 2.027777778 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x2 + 0.5) equal to 1.424000624 and -1.424000624.Subproblem 1
x2 + 0.5 = 1.424000624 Simplifying x2 + 0.5 = 1.424000624 Reorder the terms: 0.5 + x2 = 1.424000624 Solving 0.5 + x2 = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 1.424000624 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 1.424000624 + -0.5 x2 = 1.424000624 + -0.5 Combine like terms: 1.424000624 + -0.5 = 0.924000624 x2 = 0.924000624 Simplifying x2 = 0.924000624 Take the square root of each side: x = {-0.961249512, 0.961249512}Subproblem 2
x2 + 0.5 = -1.424000624 Simplifying x2 + 0.5 = -1.424000624 Reorder the terms: 0.5 + x2 = -1.424000624 Solving 0.5 + x2 = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -1.424000624 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -1.424000624 + -0.5 x2 = -1.424000624 + -0.5 Combine like terms: -1.424000624 + -0.5 = -1.924000624 x2 = -1.924000624 Simplifying x2 = -1.924000624 Reorder the terms: 1.924000624 + x2 = -1.924000624 + 1.924000624 Combine like terms: -1.924000624 + 1.924000624 = 0.000000000 1.924000624 + 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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