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Simplifying 4x2 + -17x + -26 = 8x + -1 Reorder the terms: -26 + -17x + 4x2 = 8x + -1 Reorder the terms: -26 + -17x + 4x2 = -1 + 8x Solving -26 + -17x + 4x2 = -1 + 8x Solving for variable 'x'. Reorder the terms: -26 + 1 + -17x + -8x + 4x2 = -1 + 8x + 1 + -8x Combine like terms: -26 + 1 = -25 -25 + -17x + -8x + 4x2 = -1 + 8x + 1 + -8x Combine like terms: -17x + -8x = -25x -25 + -25x + 4x2 = -1 + 8x + 1 + -8x Reorder the terms: -25 + -25x + 4x2 = -1 + 1 + 8x + -8x Combine like terms: -1 + 1 = 0 -25 + -25x + 4x2 = 0 + 8x + -8x -25 + -25x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -25 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -6.25x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -6.25x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -6.25x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -6.25x + x2 = 0 + 6.25 -6.25x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -6.25x + x2 = 6.25 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 6.25 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 6.25 + 9.765625 Combine like terms: 6.25 + 9.765625 = 16.015625 9.765625 + -6.25x + x2 = 16.015625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 16.015625 Calculate the square root of the right side: 4.001952648 Break this problem into two subproblems by setting (x + -3.125) equal to 4.001952648 and -4.001952648.Subproblem 1
x + -3.125 = 4.001952648 Simplifying x + -3.125 = 4.001952648 Reorder the terms: -3.125 + x = 4.001952648 Solving -3.125 + x = 4.001952648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 4.001952648 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 4.001952648 + 3.125 x = 4.001952648 + 3.125 Combine like terms: 4.001952648 + 3.125 = 7.126952648 x = 7.126952648 Simplifying x = 7.126952648Subproblem 2
x + -3.125 = -4.001952648 Simplifying x + -3.125 = -4.001952648 Reorder the terms: -3.125 + x = -4.001952648 Solving -3.125 + x = -4.001952648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -4.001952648 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -4.001952648 + 3.125 x = -4.001952648 + 3.125 Combine like terms: -4.001952648 + 3.125 = -0.876952648 x = -0.876952648 Simplifying x = -0.876952648Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.126952648, -0.876952648}
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