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Simplifying -1x2 + 87x = 600 Reorder the terms: 87x + -1x2 = 600 Solving 87x + -1x2 = 600 Solving for variable 'x'. Reorder the terms: -600 + 87x + -1x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 87x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 600 + -87x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -87x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -87x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -87x + x2 = 0 + -600 -87x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -87x + x2 = -600 The x term is -87x. Take half its coefficient (-43.5). Square it (1892.25) and add it to both sides. Add '1892.25' to each side of the equation. -87x + 1892.25 + x2 = -600 + 1892.25 Reorder the terms: 1892.25 + -87x + x2 = -600 + 1892.25 Combine like terms: -600 + 1892.25 = 1292.25 1892.25 + -87x + x2 = 1292.25 Factor a perfect square on the left side: (x + -43.5)(x + -43.5) = 1292.25 Calculate the square root of the right side: 35.947878936 Break this problem into two subproblems by setting (x + -43.5) equal to 35.947878936 and -35.947878936.Subproblem 1
x + -43.5 = 35.947878936 Simplifying x + -43.5 = 35.947878936 Reorder the terms: -43.5 + x = 35.947878936 Solving -43.5 + x = 35.947878936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.5' to each side of the equation. -43.5 + 43.5 + x = 35.947878936 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + x = 35.947878936 + 43.5 x = 35.947878936 + 43.5 Combine like terms: 35.947878936 + 43.5 = 79.447878936 x = 79.447878936 Simplifying x = 79.447878936Subproblem 2
x + -43.5 = -35.947878936 Simplifying x + -43.5 = -35.947878936 Reorder the terms: -43.5 + x = -35.947878936 Solving -43.5 + x = -35.947878936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.5' to each side of the equation. -43.5 + 43.5 + x = -35.947878936 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + x = -35.947878936 + 43.5 x = -35.947878936 + 43.5 Combine like terms: -35.947878936 + 43.5 = 7.552121064 x = 7.552121064 Simplifying x = 7.552121064Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.447878936, 7.552121064}
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