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Simplifying (x2) + 95x + 501 = 0 x2 + 95x + 501 = 0 Reorder the terms: 501 + 95x + x2 = 0 Solving 501 + 95x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-501' to each side of the equation. 501 + 95x + -501 + x2 = 0 + -501 Reorder the terms: 501 + -501 + 95x + x2 = 0 + -501 Combine like terms: 501 + -501 = 0 0 + 95x + x2 = 0 + -501 95x + x2 = 0 + -501 Combine like terms: 0 + -501 = -501 95x + x2 = -501 The x term is 95x. Take half its coefficient (47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. 95x + 2256.25 + x2 = -501 + 2256.25 Reorder the terms: 2256.25 + 95x + x2 = -501 + 2256.25 Combine like terms: -501 + 2256.25 = 1755.25 2256.25 + 95x + x2 = 1755.25 Factor a perfect square on the left side: (x + 47.5)(x + 47.5) = 1755.25 Calculate the square root of the right side: 41.895703837 Break this problem into two subproblems by setting (x + 47.5) equal to 41.895703837 and -41.895703837.Subproblem 1
x + 47.5 = 41.895703837 Simplifying x + 47.5 = 41.895703837 Reorder the terms: 47.5 + x = 41.895703837 Solving 47.5 + x = 41.895703837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = 41.895703837 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = 41.895703837 + -47.5 x = 41.895703837 + -47.5 Combine like terms: 41.895703837 + -47.5 = -5.604296163 x = -5.604296163 Simplifying x = -5.604296163Subproblem 2
x + 47.5 = -41.895703837 Simplifying x + 47.5 = -41.895703837 Reorder the terms: 47.5 + x = -41.895703837 Solving 47.5 + x = -41.895703837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = -41.895703837 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = -41.895703837 + -47.5 x = -41.895703837 + -47.5 Combine like terms: -41.895703837 + -47.5 = -89.395703837 x = -89.395703837 Simplifying x = -89.395703837Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.604296163, -89.395703837}
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