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Simplifying 8x6 + 99x3 + -125 = 0 Reorder the terms: -125 + 99x3 + 8x6 = 0 Solving -125 + 99x3 + 8x6 = 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'. -15.625 + 12.375x3 + x6 = 0 Move the constant term to the right: Add '15.625' to each side of the equation. -15.625 + 12.375x3 + 15.625 + x6 = 0 + 15.625 Reorder the terms: -15.625 + 15.625 + 12.375x3 + x6 = 0 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + 12.375x3 + x6 = 0 + 15.625 12.375x3 + x6 = 0 + 15.625 Combine like terms: 0 + 15.625 = 15.625 12.375x3 + x6 = 15.625 The x term is 12.375x3. Take half its coefficient (6.1875). Square it (38.28515625) and add it to both sides. Add '38.28515625' to each side of the equation. 12.375x3 + 38.28515625 + x6 = 15.625 + 38.28515625 Reorder the terms: 38.28515625 + 12.375x3 + x6 = 15.625 + 38.28515625 Combine like terms: 15.625 + 38.28515625 = 53.91015625 38.28515625 + 12.375x3 + x6 = 53.91015625 Factor a perfect square on the left side: (x3 + 6.1875)(x3 + 6.1875) = 53.91015625 Calculate the square root of the right side: 7.342353591 Break this problem into two subproblems by setting (x3 + 6.1875) equal to 7.342353591 and -7.342353591.Subproblem 1
x3 + 6.1875 = 7.342353591 Simplifying x3 + 6.1875 = 7.342353591 Reorder the terms: 6.1875 + x3 = 7.342353591 Solving 6.1875 + x3 = 7.342353591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.1875' to each side of the equation. 6.1875 + -6.1875 + x3 = 7.342353591 + -6.1875 Combine like terms: 6.1875 + -6.1875 = 0.0000 0.0000 + x3 = 7.342353591 + -6.1875 x3 = 7.342353591 + -6.1875 Combine like terms: 7.342353591 + -6.1875 = 1.154853591 x3 = 1.154853591 Simplifying x3 = 1.154853591 Reorder the terms: -1.154853591 + x3 = 1.154853591 + -1.154853591 Combine like terms: 1.154853591 + -1.154853591 = 0.000000000 -1.154853591 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 6.1875 = -7.342353591 Simplifying x3 + 6.1875 = -7.342353591 Reorder the terms: 6.1875 + x3 = -7.342353591 Solving 6.1875 + x3 = -7.342353591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.1875' to each side of the equation. 6.1875 + -6.1875 + x3 = -7.342353591 + -6.1875 Combine like terms: 6.1875 + -6.1875 = 0.0000 0.0000 + x3 = -7.342353591 + -6.1875 x3 = -7.342353591 + -6.1875 Combine like terms: -7.342353591 + -6.1875 = -13.529853591 x3 = -13.529853591 Simplifying x3 = -13.529853591 Reorder the terms: 13.529853591 + x3 = -13.529853591 + 13.529853591 Combine like terms: -13.529853591 + 13.529853591 = 0.000000000 13.529853591 + x3 = 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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