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Simplifying 2x2 + -39x + -37 = 0 Reorder the terms: -37 + -39x + 2x2 = 0 Solving -37 + -39x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18.5 + -19.5x + x2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + -19.5x + 18.5 + x2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + -19.5x + x2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + -19.5x + x2 = 0 + 18.5 -19.5x + x2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 -19.5x + x2 = 18.5 The x term is -19.5x. Take half its coefficient (-9.75). Square it (95.0625) and add it to both sides. Add '95.0625' to each side of the equation. -19.5x + 95.0625 + x2 = 18.5 + 95.0625 Reorder the terms: 95.0625 + -19.5x + x2 = 18.5 + 95.0625 Combine like terms: 18.5 + 95.0625 = 113.5625 95.0625 + -19.5x + x2 = 113.5625 Factor a perfect square on the left side: (x + -9.75)(x + -9.75) = 113.5625 Calculate the square root of the right side: 10.656570743 Break this problem into two subproblems by setting (x + -9.75) equal to 10.656570743 and -10.656570743.Subproblem 1
x + -9.75 = 10.656570743 Simplifying x + -9.75 = 10.656570743 Reorder the terms: -9.75 + x = 10.656570743 Solving -9.75 + x = 10.656570743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = 10.656570743 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = 10.656570743 + 9.75 x = 10.656570743 + 9.75 Combine like terms: 10.656570743 + 9.75 = 20.406570743 x = 20.406570743 Simplifying x = 20.406570743Subproblem 2
x + -9.75 = -10.656570743 Simplifying x + -9.75 = -10.656570743 Reorder the terms: -9.75 + x = -10.656570743 Solving -9.75 + x = -10.656570743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.75' to each side of the equation. -9.75 + 9.75 + x = -10.656570743 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + x = -10.656570743 + 9.75 x = -10.656570743 + 9.75 Combine like terms: -10.656570743 + 9.75 = -0.906570743 x = -0.906570743 Simplifying x = -0.906570743Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.406570743, -0.906570743}
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