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Simplifying -13x2 + 624x + -5000 = 0 Reorder the terms: -5000 + 624x + -13x2 = 0 Solving -5000 + 624x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. 384.6153846 + -48x + x2 = 0 Move the constant term to the right: Add '-384.6153846' to each side of the equation. 384.6153846 + -48x + -384.6153846 + x2 = 0 + -384.6153846 Reorder the terms: 384.6153846 + -384.6153846 + -48x + x2 = 0 + -384.6153846 Combine like terms: 384.6153846 + -384.6153846 = 0.0000000 0.0000000 + -48x + x2 = 0 + -384.6153846 -48x + x2 = 0 + -384.6153846 Combine like terms: 0 + -384.6153846 = -384.6153846 -48x + x2 = -384.6153846 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 = -384.6153846 + 576 Reorder the terms: 576 + -48x + x2 = -384.6153846 + 576 Combine like terms: -384.6153846 + 576 = 191.3846154 576 + -48x + x2 = 191.3846154 Factor a perfect square on the left side: (x + -24)(x + -24) = 191.3846154 Calculate the square root of the right side: 13.83418286 Break this problem into two subproblems by setting (x + -24) equal to 13.83418286 and -13.83418286.Subproblem 1
x + -24 = 13.83418286 Simplifying x + -24 = 13.83418286 Reorder the terms: -24 + x = 13.83418286 Solving -24 + x = 13.83418286 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 = 13.83418286 + 24 Combine like terms: -24 + 24 = 0 0 + x = 13.83418286 + 24 x = 13.83418286 + 24 Combine like terms: 13.83418286 + 24 = 37.83418286 x = 37.83418286 Simplifying x = 37.83418286Subproblem 2
x + -24 = -13.83418286 Simplifying x + -24 = -13.83418286 Reorder the terms: -24 + x = -13.83418286 Solving -24 + x = -13.83418286 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 = -13.83418286 + 24 Combine like terms: -24 + 24 = 0 0 + x = -13.83418286 + 24 x = -13.83418286 + 24 Combine like terms: -13.83418286 + 24 = 10.16581714 x = 10.16581714 Simplifying x = 10.16581714Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.83418286, 10.16581714}
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