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Simplifying (175 + x)(175 + x) + x * x = 75625 Multiply (175 + x) * (175 + x) (175(175 + x) + x(175 + x)) + x * x = 75625 ((175 * 175 + x * 175) + x(175 + x)) + x * x = 75625 ((30625 + 175x) + x(175 + x)) + x * x = 75625 (30625 + 175x + (175 * x + x * x)) + x * x = 75625 (30625 + 175x + (175x + x2)) + x * x = 75625 Combine like terms: 175x + 175x = 350x (30625 + 350x + x2) + x * x = 75625 Multiply x * x 30625 + 350x + x2 + x2 = 75625 Combine like terms: x2 + x2 = 2x2 30625 + 350x + 2x2 = 75625 Solving 30625 + 350x + 2x2 = 75625 Solving for variable 'x'. Reorder the terms: 30625 + -75625 + 350x + 2x2 = 75625 + -75625 Combine like terms: 30625 + -75625 = -45000 -45000 + 350x + 2x2 = 75625 + -75625 Combine like terms: 75625 + -75625 = 0 -45000 + 350x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-22500 + 175x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22500 + 175x + x2)' equal to zero and attempt to solve: Simplifying -22500 + 175x + x2 = 0 Solving -22500 + 175x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22500' to each side of the equation. -22500 + 175x + 22500 + x2 = 0 + 22500 Reorder the terms: -22500 + 22500 + 175x + x2 = 0 + 22500 Combine like terms: -22500 + 22500 = 0 0 + 175x + x2 = 0 + 22500 175x + x2 = 0 + 22500 Combine like terms: 0 + 22500 = 22500 175x + x2 = 22500 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 = 22500 + 7656.25 Reorder the terms: 7656.25 + 175x + x2 = 22500 + 7656.25 Combine like terms: 22500 + 7656.25 = 30156.25 7656.25 + 175x + x2 = 30156.25 Factor a perfect square on the left side: (x + 87.5)(x + 87.5) = 30156.25 Calculate the square root of the right side: 173.655549868 Break this problem into two subproblems by setting (x + 87.5) equal to 173.655549868 and -173.655549868.Subproblem 1
x + 87.5 = 173.655549868 Simplifying x + 87.5 = 173.655549868 Reorder the terms: 87.5 + x = 173.655549868 Solving 87.5 + x = 173.655549868 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 = 173.655549868 + -87.5 Combine like terms: 87.5 + -87.5 = 0.0 0.0 + x = 173.655549868 + -87.5 x = 173.655549868 + -87.5 Combine like terms: 173.655549868 + -87.5 = 86.155549868 x = 86.155549868 Simplifying x = 86.155549868Subproblem 2
x + 87.5 = -173.655549868 Simplifying x + 87.5 = -173.655549868 Reorder the terms: 87.5 + x = -173.655549868 Solving 87.5 + x = -173.655549868 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 = -173.655549868 + -87.5 Combine like terms: 87.5 + -87.5 = 0.0 0.0 + x = -173.655549868 + -87.5 x = -173.655549868 + -87.5 Combine like terms: -173.655549868 + -87.5 = -261.155549868 x = -261.155549868 Simplifying x = -261.155549868Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.155549868, -261.155549868}Solution
x = {86.155549868, -261.155549868}
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