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Simplifying 0.5x2 + -15x + 172 = 2x + 37 Reorder the terms: 172 + -15x + 0.5x2 = 2x + 37 Reorder the terms: 172 + -15x + 0.5x2 = 37 + 2x Solving 172 + -15x + 0.5x2 = 37 + 2x Solving for variable 'x'. Reorder the terms: 172 + -37 + -15x + -2x + 0.5x2 = 37 + 2x + -37 + -2x Combine like terms: 172 + -37 = 135 135 + -15x + -2x + 0.5x2 = 37 + 2x + -37 + -2x Combine like terms: -15x + -2x = -17x 135 + -17x + 0.5x2 = 37 + 2x + -37 + -2x Reorder the terms: 135 + -17x + 0.5x2 = 37 + -37 + 2x + -2x Combine like terms: 37 + -37 = 0 135 + -17x + 0.5x2 = 0 + 2x + -2x 135 + -17x + 0.5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 135 + -17x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 270 + -34x + x2 = 0 Move the constant term to the right: Add '-270' to each side of the equation. 270 + -34x + -270 + x2 = 0 + -270 Reorder the terms: 270 + -270 + -34x + x2 = 0 + -270 Combine like terms: 270 + -270 = 0 0 + -34x + x2 = 0 + -270 -34x + x2 = 0 + -270 Combine like terms: 0 + -270 = -270 -34x + x2 = -270 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -270 + 289 Reorder the terms: 289 + -34x + x2 = -270 + 289 Combine like terms: -270 + 289 = 19 289 + -34x + x2 = 19 Factor a perfect square on the left side: (x + -17)(x + -17) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -17) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -17 = 4.358898944 Simplifying x + -17 = 4.358898944 Reorder the terms: -17 + x = 4.358898944 Solving -17 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 4.358898944 + 17 Combine like terms: -17 + 17 = 0 0 + x = 4.358898944 + 17 x = 4.358898944 + 17 Combine like terms: 4.358898944 + 17 = 21.358898944 x = 21.358898944 Simplifying x = 21.358898944Subproblem 2
x + -17 = -4.358898944 Simplifying x + -17 = -4.358898944 Reorder the terms: -17 + x = -4.358898944 Solving -17 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -4.358898944 + 17 Combine like terms: -17 + 17 = 0 0 + x = -4.358898944 + 17 x = -4.358898944 + 17 Combine like terms: -4.358898944 + 17 = 12.641101056 x = 12.641101056 Simplifying x = 12.641101056Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.358898944, 12.641101056}
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