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Simplifying 5x(x + -23) = -37 Reorder the terms: 5x(-23 + x) = -37 (-23 * 5x + x * 5x) = -37 (-115x + 5x2) = -37 Solving -115x + 5x2 = -37 Solving for variable 'x'. Reorder the terms: 37 + -115x + 5x2 = -37 + 37 Combine like terms: -37 + 37 = 0 37 + -115x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.4 + -23x + x2 = 0 Move the constant term to the right: Add '-7.4' to each side of the equation. 7.4 + -23x + -7.4 + x2 = 0 + -7.4 Reorder the terms: 7.4 + -7.4 + -23x + x2 = 0 + -7.4 Combine like terms: 7.4 + -7.4 = 0.0 0.0 + -23x + x2 = 0 + -7.4 -23x + x2 = 0 + -7.4 Combine like terms: 0 + -7.4 = -7.4 -23x + x2 = -7.4 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -7.4 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -7.4 + 132.25 Combine like terms: -7.4 + 132.25 = 124.85 132.25 + -23x + x2 = 124.85 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 124.85 Calculate the square root of the right side: 11.17362967 Break this problem into two subproblems by setting (x + -11.5) equal to 11.17362967 and -11.17362967.Subproblem 1
x + -11.5 = 11.17362967 Simplifying x + -11.5 = 11.17362967 Reorder the terms: -11.5 + x = 11.17362967 Solving -11.5 + x = 11.17362967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.17362967 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.17362967 + 11.5 x = 11.17362967 + 11.5 Combine like terms: 11.17362967 + 11.5 = 22.67362967 x = 22.67362967 Simplifying x = 22.67362967Subproblem 2
x + -11.5 = -11.17362967 Simplifying x + -11.5 = -11.17362967 Reorder the terms: -11.5 + x = -11.17362967 Solving -11.5 + x = -11.17362967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.17362967 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.17362967 + 11.5 x = -11.17362967 + 11.5 Combine like terms: -11.17362967 + 11.5 = 0.32637033 x = 0.32637033 Simplifying x = 0.32637033Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.67362967, 0.32637033}
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