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Simplifying x(4x + -630) = 3815 Reorder the terms: x(-630 + 4x) = 3815 (-630 * x + 4x * x) = 3815 (-630x + 4x2) = 3815 Solving -630x + 4x2 = 3815 Solving for variable 'x'. Reorder the terms: -3815 + -630x + 4x2 = 3815 + -3815 Combine like terms: 3815 + -3815 = 0 -3815 + -630x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -953.75 + -157.5x + x2 = 0 Move the constant term to the right: Add '953.75' to each side of the equation. -953.75 + -157.5x + 953.75 + x2 = 0 + 953.75 Reorder the terms: -953.75 + 953.75 + -157.5x + x2 = 0 + 953.75 Combine like terms: -953.75 + 953.75 = 0.00 0.00 + -157.5x + x2 = 0 + 953.75 -157.5x + x2 = 0 + 953.75 Combine like terms: 0 + 953.75 = 953.75 -157.5x + x2 = 953.75 The x term is -157.5x. Take half its coefficient (-78.75). Square it (6201.5625) and add it to both sides. Add '6201.5625' to each side of the equation. -157.5x + 6201.5625 + x2 = 953.75 + 6201.5625 Reorder the terms: 6201.5625 + -157.5x + x2 = 953.75 + 6201.5625 Combine like terms: 953.75 + 6201.5625 = 7155.3125 6201.5625 + -157.5x + x2 = 7155.3125 Factor a perfect square on the left side: (x + -78.75)(x + -78.75) = 7155.3125 Calculate the square root of the right side: 84.589080265 Break this problem into two subproblems by setting (x + -78.75) equal to 84.589080265 and -84.589080265.Subproblem 1
x + -78.75 = 84.589080265 Simplifying x + -78.75 = 84.589080265 Reorder the terms: -78.75 + x = 84.589080265 Solving -78.75 + x = 84.589080265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '78.75' to each side of the equation. -78.75 + 78.75 + x = 84.589080265 + 78.75 Combine like terms: -78.75 + 78.75 = 0.00 0.00 + x = 84.589080265 + 78.75 x = 84.589080265 + 78.75 Combine like terms: 84.589080265 + 78.75 = 163.339080265 x = 163.339080265 Simplifying x = 163.339080265Subproblem 2
x + -78.75 = -84.589080265 Simplifying x + -78.75 = -84.589080265 Reorder the terms: -78.75 + x = -84.589080265 Solving -78.75 + x = -84.589080265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '78.75' to each side of the equation. -78.75 + 78.75 + x = -84.589080265 + 78.75 Combine like terms: -78.75 + 78.75 = 0.00 0.00 + x = -84.589080265 + 78.75 x = -84.589080265 + 78.75 Combine like terms: -84.589080265 + 78.75 = -5.839080265 x = -5.839080265 Simplifying x = -5.839080265Solution
The solution to the problem is based on the solutions from the subproblems. x = {163.339080265, -5.839080265}
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