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Simplifying -5x2 + 240x + -2635 = 24 Reorder the terms: -2635 + 240x + -5x2 = 24 Solving -2635 + 240x + -5x2 = 24 Solving for variable 'x'. Reorder the terms: -2635 + -24 + 240x + -5x2 = 24 + -24 Combine like terms: -2635 + -24 = -2659 -2659 + 240x + -5x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -2659 + 240x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 531.8 + -48x + x2 = 0 Move the constant term to the right: Add '-531.8' to each side of the equation. 531.8 + -48x + -531.8 + x2 = 0 + -531.8 Reorder the terms: 531.8 + -531.8 + -48x + x2 = 0 + -531.8 Combine like terms: 531.8 + -531.8 = 0.0 0.0 + -48x + x2 = 0 + -531.8 -48x + x2 = 0 + -531.8 Combine like terms: 0 + -531.8 = -531.8 -48x + x2 = -531.8 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = -531.8 + 576 Reorder the terms: 576 + -48x + x2 = -531.8 + 576 Combine like terms: -531.8 + 576 = 44.2 576 + -48x + x2 = 44.2 Factor a perfect square on the left side: (x + -24)(x + -24) = 44.2 Calculate the square root of the right side: 6.648308055 Break this problem into two subproblems by setting (x + -24) equal to 6.648308055 and -6.648308055.Subproblem 1
x + -24 = 6.648308055 Simplifying x + -24 = 6.648308055 Reorder the terms: -24 + x = 6.648308055 Solving -24 + x = 6.648308055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 6.648308055 + 24 Combine like terms: -24 + 24 = 0 0 + x = 6.648308055 + 24 x = 6.648308055 + 24 Combine like terms: 6.648308055 + 24 = 30.648308055 x = 30.648308055 Simplifying x = 30.648308055Subproblem 2
x + -24 = -6.648308055 Simplifying x + -24 = -6.648308055 Reorder the terms: -24 + x = -6.648308055 Solving -24 + x = -6.648308055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -6.648308055 + 24 Combine like terms: -24 + 24 = 0 0 + x = -6.648308055 + 24 x = -6.648308055 + 24 Combine like terms: -6.648308055 + 24 = 17.351691945 x = 17.351691945 Simplifying x = 17.351691945Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.648308055, 17.351691945}
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