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Simplifying (x)(x + 65) = 63.9 Reorder the terms: x(65 + x) = 63.9 (65 * x + x * x) = 63.9 (65x + x2) = 63.9 Solving 65x + x2 = 63.9 Solving for variable 'x'. Reorder the terms: -63.9 + 65x + x2 = 63.9 + -63.9 Combine like terms: 63.9 + -63.9 = 0.0 -63.9 + 65x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '63.9' to each side of the equation. -63.9 + 65x + 63.9 + x2 = 0.0 + 63.9 Reorder the terms: -63.9 + 63.9 + 65x + x2 = 0.0 + 63.9 Combine like terms: -63.9 + 63.9 = 0.0 0.0 + 65x + x2 = 0.0 + 63.9 65x + x2 = 0.0 + 63.9 Combine like terms: 0.0 + 63.9 = 63.9 65x + x2 = 63.9 The x term is 65x. Take half its coefficient (32.5). Square it (1056.25) and add it to both sides. Add '1056.25' to each side of the equation. 65x + 1056.25 + x2 = 63.9 + 1056.25 Reorder the terms: 1056.25 + 65x + x2 = 63.9 + 1056.25 Combine like terms: 63.9 + 1056.25 = 1120.15 1056.25 + 65x + x2 = 1120.15 Factor a perfect square on the left side: (x + 32.5)(x + 32.5) = 1120.15 Calculate the square root of the right side: 33.46864204 Break this problem into two subproblems by setting (x + 32.5) equal to 33.46864204 and -33.46864204.Subproblem 1
x + 32.5 = 33.46864204 Simplifying x + 32.5 = 33.46864204 Reorder the terms: 32.5 + x = 33.46864204 Solving 32.5 + x = 33.46864204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.5' to each side of the equation. 32.5 + -32.5 + x = 33.46864204 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = 33.46864204 + -32.5 x = 33.46864204 + -32.5 Combine like terms: 33.46864204 + -32.5 = 0.96864204 x = 0.96864204 Simplifying x = 0.96864204Subproblem 2
x + 32.5 = -33.46864204 Simplifying x + 32.5 = -33.46864204 Reorder the terms: 32.5 + x = -33.46864204 Solving 32.5 + x = -33.46864204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.5' to each side of the equation. 32.5 + -32.5 + x = -33.46864204 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = -33.46864204 + -32.5 x = -33.46864204 + -32.5 Combine like terms: -33.46864204 + -32.5 = -65.96864204 x = -65.96864204 Simplifying x = -65.96864204Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96864204, -65.96864204}
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