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Simplifying (2x + -3)(x) = 317 Reorder the terms: (-3 + 2x)(x) = 317 Reorder the terms for easier multiplication: x(-3 + 2x) = 317 (-3 * x + 2x * x) = 317 (-3x + 2x2) = 317 Solving -3x + 2x2 = 317 Solving for variable 'x'. Reorder the terms: -317 + -3x + 2x2 = 317 + -317 Combine like terms: 317 + -317 = 0 -317 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -158.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '158.5' to each side of the equation. -158.5 + -1.5x + 158.5 + x2 = 0 + 158.5 Reorder the terms: -158.5 + 158.5 + -1.5x + x2 = 0 + 158.5 Combine like terms: -158.5 + 158.5 = 0.0 0.0 + -1.5x + x2 = 0 + 158.5 -1.5x + x2 = 0 + 158.5 Combine like terms: 0 + 158.5 = 158.5 -1.5x + x2 = 158.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 158.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 158.5 + 0.5625 Combine like terms: 158.5 + 0.5625 = 159.0625 0.5625 + -1.5x + x2 = 159.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 159.0625 Calculate the square root of the right side: 12.611998256 Break this problem into two subproblems by setting (x + -0.75) equal to 12.611998256 and -12.611998256.Subproblem 1
x + -0.75 = 12.611998256 Simplifying x + -0.75 = 12.611998256 Reorder the terms: -0.75 + x = 12.611998256 Solving -0.75 + x = 12.611998256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 12.611998256 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 12.611998256 + 0.75 x = 12.611998256 + 0.75 Combine like terms: 12.611998256 + 0.75 = 13.361998256 x = 13.361998256 Simplifying x = 13.361998256Subproblem 2
x + -0.75 = -12.611998256 Simplifying x + -0.75 = -12.611998256 Reorder the terms: -0.75 + x = -12.611998256 Solving -0.75 + x = -12.611998256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -12.611998256 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -12.611998256 + 0.75 x = -12.611998256 + 0.75 Combine like terms: -12.611998256 + 0.75 = -11.861998256 x = -11.861998256 Simplifying x = -11.861998256Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.361998256, -11.861998256}
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