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Simplifying x2 + 29x = 180 Reorder the terms: 29x + x2 = 180 Solving 29x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 29x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 29x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 29x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 29x + x2 = 0 + 180 29x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 29x + x2 = 180 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 180 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 180 + 210.25 Combine like terms: 180 + 210.25 = 390.25 210.25 + 29x + x2 = 390.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 390.25 Calculate the square root of the right side: 19.754746265 Break this problem into two subproblems by setting (x + 14.5) equal to 19.754746265 and -19.754746265.Subproblem 1
x + 14.5 = 19.754746265 Simplifying x + 14.5 = 19.754746265 Reorder the terms: 14.5 + x = 19.754746265 Solving 14.5 + x = 19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 19.754746265 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 19.754746265 + -14.5 x = 19.754746265 + -14.5 Combine like terms: 19.754746265 + -14.5 = 5.254746265 x = 5.254746265 Simplifying x = 5.254746265Subproblem 2
x + 14.5 = -19.754746265 Simplifying x + 14.5 = -19.754746265 Reorder the terms: 14.5 + x = -19.754746265 Solving 14.5 + x = -19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -19.754746265 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -19.754746265 + -14.5 x = -19.754746265 + -14.5 Combine like terms: -19.754746265 + -14.5 = -34.254746265 x = -34.254746265 Simplifying x = -34.254746265Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.254746265, -34.254746265}
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