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Simplifying 9x4 + x2 + -200 = 0 Reorder the terms: -200 + x2 + 9x4 = 0 Solving -200 + x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -22.22222222 + 0.1111111111x2 + x4 = 0 Move the constant term to the right: Add '22.22222222' to each side of the equation. -22.22222222 + 0.1111111111x2 + 22.22222222 + x4 = 0 + 22.22222222 Reorder the terms: -22.22222222 + 22.22222222 + 0.1111111111x2 + x4 = 0 + 22.22222222 Combine like terms: -22.22222222 + 22.22222222 = 0.00000000 0.00000000 + 0.1111111111x2 + x4 = 0 + 22.22222222 0.1111111111x2 + x4 = 0 + 22.22222222 Combine like terms: 0 + 22.22222222 = 22.22222222 0.1111111111x2 + x4 = 22.22222222 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. 0.1111111111x2 + 0.25 + x4 = 22.22222222 + 0.25 Reorder the terms: 0.25 + 0.1111111111x2 + x4 = 22.22222222 + 0.25 Combine like terms: 22.22222222 + 0.25 = 22.47222222 0.25 + 0.1111111111x2 + x4 = 22.47222222 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 22.47222222 Calculate the square root of the right side: 4.740487551 Break this problem into two subproblems by setting (x2 + 0.5) equal to 4.740487551 and -4.740487551.Subproblem 1
x2 + 0.5 = 4.740487551 Simplifying x2 + 0.5 = 4.740487551 Reorder the terms: 0.5 + x2 = 4.740487551 Solving 0.5 + x2 = 4.740487551 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 = 4.740487551 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 4.740487551 + -0.5 x2 = 4.740487551 + -0.5 Combine like terms: 4.740487551 + -0.5 = 4.240487551 x2 = 4.240487551 Simplifying x2 = 4.240487551 Take the square root of each side: x = {-2.059244413, 2.059244413}Subproblem 2
x2 + 0.5 = -4.740487551 Simplifying x2 + 0.5 = -4.740487551 Reorder the terms: 0.5 + x2 = -4.740487551 Solving 0.5 + x2 = -4.740487551 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 = -4.740487551 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -4.740487551 + -0.5 x2 = -4.740487551 + -0.5 Combine like terms: -4.740487551 + -0.5 = -5.240487551 x2 = -5.240487551 Simplifying x2 = -5.240487551 Reorder the terms: 5.240487551 + x2 = -5.240487551 + 5.240487551 Combine like terms: -5.240487551 + 5.240487551 = 0.000000000 5.240487551 + 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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