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Simplifying x(175 + x) = 30625 (175 * x + x * x) = 30625 (175x + x2) = 30625 Solving 175x + x2 = 30625 Solving for variable 'x'. Reorder the terms: -30625 + 175x + x2 = 30625 + -30625 Combine like terms: 30625 + -30625 = 0 -30625 + 175x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30625' to each side of the equation. -30625 + 175x + 30625 + x2 = 0 + 30625 Reorder the terms: -30625 + 30625 + 175x + x2 = 0 + 30625 Combine like terms: -30625 + 30625 = 0 0 + 175x + x2 = 0 + 30625 175x + x2 = 0 + 30625 Combine like terms: 0 + 30625 = 30625 175x + x2 = 30625 The x term is 175x. Take half its coefficient (87.5). Square it (7656.25) and add it to both sides. Add '7656.25' to each side of the equation. 175x + 7656.25 + x2 = 30625 + 7656.25 Reorder the terms: 7656.25 + 175x + x2 = 30625 + 7656.25 Combine like terms: 30625 + 7656.25 = 38281.25 7656.25 + 175x + x2 = 38281.25 Factor a perfect square on the left side: (x + 87.5)(x + 87.5) = 38281.25 Calculate the square root of the right side: 195.655948031 Break this problem into two subproblems by setting (x + 87.5) equal to 195.655948031 and -195.655948031.Subproblem 1
x + 87.5 = 195.655948031 Simplifying x + 87.5 = 195.655948031 Reorder the terms: 87.5 + x = 195.655948031 Solving 87.5 + x = 195.655948031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-87.5' to each side of the equation. 87.5 + -87.5 + x = 195.655948031 + -87.5 Combine like terms: 87.5 + -87.5 = 0.0 0.0 + x = 195.655948031 + -87.5 x = 195.655948031 + -87.5 Combine like terms: 195.655948031 + -87.5 = 108.155948031 x = 108.155948031 Simplifying x = 108.155948031Subproblem 2
x + 87.5 = -195.655948031 Simplifying x + 87.5 = -195.655948031 Reorder the terms: 87.5 + x = -195.655948031 Solving 87.5 + x = -195.655948031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-87.5' to each side of the equation. 87.5 + -87.5 + x = -195.655948031 + -87.5 Combine like terms: 87.5 + -87.5 = 0.0 0.0 + x = -195.655948031 + -87.5 x = -195.655948031 + -87.5 Combine like terms: -195.655948031 + -87.5 = -283.155948031 x = -283.155948031 Simplifying x = -283.155948031Solution
The solution to the problem is based on the solutions from the subproblems. x = {108.155948031, -283.155948031}
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