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Simplifying -55x2 + -2062.5x + 18342.5 = 0 Reorder the terms: 18342.5 + -2062.5x + -55x2 = 0 Solving 18342.5 + -2062.5x + -55x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -55 the coefficient of the squared term: Divide each side by '-55'. -333.5 + 37.5x + x2 = 0 Move the constant term to the right: Add '333.5' to each side of the equation. -333.5 + 37.5x + 333.5 + x2 = 0 + 333.5 Reorder the terms: -333.5 + 333.5 + 37.5x + x2 = 0 + 333.5 Combine like terms: -333.5 + 333.5 = 0.0 0.0 + 37.5x + x2 = 0 + 333.5 37.5x + x2 = 0 + 333.5 Combine like terms: 0 + 333.5 = 333.5 37.5x + x2 = 333.5 The x term is 37.5x. Take half its coefficient (18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. 37.5x + 351.5625 + x2 = 333.5 + 351.5625 Reorder the terms: 351.5625 + 37.5x + x2 = 333.5 + 351.5625 Combine like terms: 333.5 + 351.5625 = 685.0625 351.5625 + 37.5x + x2 = 685.0625 Factor a perfect square on the left side: (x + 18.75)(x + 18.75) = 685.0625 Calculate the square root of the right side: 26.17369863 Break this problem into two subproblems by setting (x + 18.75) equal to 26.17369863 and -26.17369863.Subproblem 1
x + 18.75 = 26.17369863 Simplifying x + 18.75 = 26.17369863 Reorder the terms: 18.75 + x = 26.17369863 Solving 18.75 + x = 26.17369863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 26.17369863 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 26.17369863 + -18.75 x = 26.17369863 + -18.75 Combine like terms: 26.17369863 + -18.75 = 7.42369863 x = 7.42369863 Simplifying x = 7.42369863Subproblem 2
x + 18.75 = -26.17369863 Simplifying x + 18.75 = -26.17369863 Reorder the terms: 18.75 + x = -26.17369863 Solving 18.75 + x = -26.17369863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -26.17369863 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -26.17369863 + -18.75 x = -26.17369863 + -18.75 Combine like terms: -26.17369863 + -18.75 = -44.92369863 x = -44.92369863 Simplifying x = -44.92369863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.42369863, -44.92369863}
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