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Simplifying 8x2 + -3x = 17x + -3 Reorder the terms: -3x + 8x2 = 17x + -3 Reorder the terms: -3x + 8x2 = -3 + 17x Solving -3x + 8x2 = -3 + 17x Solving for variable 'x'. Reorder the terms: 3 + -3x + -17x + 8x2 = -3 + 17x + 3 + -17x Combine like terms: -3x + -17x = -20x 3 + -20x + 8x2 = -3 + 17x + 3 + -17x Reorder the terms: 3 + -20x + 8x2 = -3 + 3 + 17x + -17x Combine like terms: -3 + 3 = 0 3 + -20x + 8x2 = 0 + 17x + -17x 3 + -20x + 8x2 = 17x + -17x Combine like terms: 17x + -17x = 0 3 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -2.5x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -2.5x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -2.5x + x2 = 0 + -0.375 -2.5x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -2.5x + x2 = -0.375 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.375 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.375 + 1.5625 Combine like terms: -0.375 + 1.5625 = 1.1875 1.5625 + -2.5x + x2 = 1.1875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.1875 Calculate the square root of the right side: 1.089724736 Break this problem into two subproblems by setting (x + -1.25) equal to 1.089724736 and -1.089724736.Subproblem 1
x + -1.25 = 1.089724736 Simplifying x + -1.25 = 1.089724736 Reorder the terms: -1.25 + x = 1.089724736 Solving -1.25 + x = 1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.089724736 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.089724736 + 1.25 x = 1.089724736 + 1.25 Combine like terms: 1.089724736 + 1.25 = 2.339724736 x = 2.339724736 Simplifying x = 2.339724736Subproblem 2
x + -1.25 = -1.089724736 Simplifying x + -1.25 = -1.089724736 Reorder the terms: -1.25 + x = -1.089724736 Solving -1.25 + x = -1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.089724736 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.089724736 + 1.25 x = -1.089724736 + 1.25 Combine like terms: -1.089724736 + 1.25 = 0.160275264 x = 0.160275264 Simplifying x = 0.160275264Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.339724736, 0.160275264}
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