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Simplifying -1x2 + 31x + -8 = 0 Reorder the terms: -8 + 31x + -1x2 = 0 Solving -8 + 31x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -31x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -31x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -31x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -31x + x2 = 0 + -8 -31x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -31x + x2 = -8 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = -8 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -8 + 240.25 Combine like terms: -8 + 240.25 = 232.25 240.25 + -31x + x2 = 232.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 232.25 Calculate the square root of the right side: 15.239750654 Break this problem into two subproblems by setting (x + -15.5) equal to 15.239750654 and -15.239750654.Subproblem 1
x + -15.5 = 15.239750654 Simplifying x + -15.5 = 15.239750654 Reorder the terms: -15.5 + x = 15.239750654 Solving -15.5 + x = 15.239750654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 15.239750654 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 15.239750654 + 15.5 x = 15.239750654 + 15.5 Combine like terms: 15.239750654 + 15.5 = 30.739750654 x = 30.739750654 Simplifying x = 30.739750654Subproblem 2
x + -15.5 = -15.239750654 Simplifying x + -15.5 = -15.239750654 Reorder the terms: -15.5 + x = -15.239750654 Solving -15.5 + x = -15.239750654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -15.239750654 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -15.239750654 + 15.5 x = -15.239750654 + 15.5 Combine like terms: -15.239750654 + 15.5 = 0.260249346 x = 0.260249346 Simplifying x = 0.260249346Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.739750654, 0.260249346}
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