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Simplifying 2x2 + -75x + 63 = 0 Reorder the terms: 63 + -75x + 2x2 = 0 Solving 63 + -75x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 31.5 + -37.5x + x2 = 0 Move the constant term to the right: Add '-31.5' to each side of the equation. 31.5 + -37.5x + -31.5 + x2 = 0 + -31.5 Reorder the terms: 31.5 + -31.5 + -37.5x + x2 = 0 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + -37.5x + x2 = 0 + -31.5 -37.5x + x2 = 0 + -31.5 Combine like terms: 0 + -31.5 = -31.5 -37.5x + x2 = -31.5 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 = -31.5 + 351.5625 Reorder the terms: 351.5625 + -37.5x + x2 = -31.5 + 351.5625 Combine like terms: -31.5 + 351.5625 = 320.0625 351.5625 + -37.5x + x2 = 320.0625 Factor a perfect square on the left side: (x + -18.75)(x + -18.75) = 320.0625 Calculate the square root of the right side: 17.890290663 Break this problem into two subproblems by setting (x + -18.75) equal to 17.890290663 and -17.890290663.Subproblem 1
x + -18.75 = 17.890290663 Simplifying x + -18.75 = 17.890290663 Reorder the terms: -18.75 + x = 17.890290663 Solving -18.75 + x = 17.890290663 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 = 17.890290663 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 17.890290663 + 18.75 x = 17.890290663 + 18.75 Combine like terms: 17.890290663 + 18.75 = 36.640290663 x = 36.640290663 Simplifying x = 36.640290663Subproblem 2
x + -18.75 = -17.890290663 Simplifying x + -18.75 = -17.890290663 Reorder the terms: -18.75 + x = -17.890290663 Solving -18.75 + x = -17.890290663 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 = -17.890290663 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = -17.890290663 + 18.75 x = -17.890290663 + 18.75 Combine like terms: -17.890290663 + 18.75 = 0.859709337 x = 0.859709337 Simplifying x = 0.859709337Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.640290663, 0.859709337}
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