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Simplifying 129 = x + 2x(x + 17) Reorder the terms: 129 = x + 2x(17 + x) 129 = x + (17 * 2x + x * 2x) 129 = x + (34x + 2x2) Combine like terms: x + 34x = 35x 129 = 35x + 2x2 Solving 129 = 35x + 2x2 Solving for variable 'x'. Reorder the terms: 129 + -35x + -2x2 = 35x + -35x + 2x2 + -2x2 Combine like terms: 35x + -35x = 0 129 + -35x + -2x2 = 0 + 2x2 + -2x2 129 + -35x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 129 + -35x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -64.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '64.5' to each side of the equation. -64.5 + 17.5x + 64.5 + x2 = 0 + 64.5 Reorder the terms: -64.5 + 64.5 + 17.5x + x2 = 0 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + 17.5x + x2 = 0 + 64.5 17.5x + x2 = 0 + 64.5 Combine like terms: 0 + 64.5 = 64.5 17.5x + x2 = 64.5 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 64.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 64.5 + 76.5625 Combine like terms: 64.5 + 76.5625 = 141.0625 76.5625 + 17.5x + x2 = 141.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 141.0625 Calculate the square root of the right side: 11.87697352 Break this problem into two subproblems by setting (x + 8.75) equal to 11.87697352 and -11.87697352.Subproblem 1
x + 8.75 = 11.87697352 Simplifying x + 8.75 = 11.87697352 Reorder the terms: 8.75 + x = 11.87697352 Solving 8.75 + x = 11.87697352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 11.87697352 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 11.87697352 + -8.75 x = 11.87697352 + -8.75 Combine like terms: 11.87697352 + -8.75 = 3.12697352 x = 3.12697352 Simplifying x = 3.12697352Subproblem 2
x + 8.75 = -11.87697352 Simplifying x + 8.75 = -11.87697352 Reorder the terms: 8.75 + x = -11.87697352 Solving 8.75 + x = -11.87697352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -11.87697352 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -11.87697352 + -8.75 x = -11.87697352 + -8.75 Combine like terms: -11.87697352 + -8.75 = -20.62697352 x = -20.62697352 Simplifying x = -20.62697352Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.12697352, -20.62697352}
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