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Simplifying 5x(3x + 17) = 2(-8 + -1x) Reorder the terms: 5x(17 + 3x) = 2(-8 + -1x) (17 * 5x + 3x * 5x) = 2(-8 + -1x) (85x + 15x2) = 2(-8 + -1x) 85x + 15x2 = (-8 * 2 + -1x * 2) 85x + 15x2 = (-16 + -2x) Solving 85x + 15x2 = -16 + -2x Solving for variable 'x'. Reorder the terms: 16 + 85x + 2x + 15x2 = -16 + -2x + 16 + 2x Combine like terms: 85x + 2x = 87x 16 + 87x + 15x2 = -16 + -2x + 16 + 2x Reorder the terms: 16 + 87x + 15x2 = -16 + 16 + -2x + 2x Combine like terms: -16 + 16 = 0 16 + 87x + 15x2 = 0 + -2x + 2x 16 + 87x + 15x2 = -2x + 2x Combine like terms: -2x + 2x = 0 16 + 87x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.066666667 + 5.8x + x2 = 0 Move the constant term to the right: Add '-1.066666667' to each side of the equation. 1.066666667 + 5.8x + -1.066666667 + x2 = 0 + -1.066666667 Reorder the terms: 1.066666667 + -1.066666667 + 5.8x + x2 = 0 + -1.066666667 Combine like terms: 1.066666667 + -1.066666667 = 0.000000000 0.000000000 + 5.8x + x2 = 0 + -1.066666667 5.8x + x2 = 0 + -1.066666667 Combine like terms: 0 + -1.066666667 = -1.066666667 5.8x + x2 = -1.066666667 The x term is 5.8x. Take half its coefficient (2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. 5.8x + 8.41 + x2 = -1.066666667 + 8.41 Reorder the terms: 8.41 + 5.8x + x2 = -1.066666667 + 8.41 Combine like terms: -1.066666667 + 8.41 = 7.343333333 8.41 + 5.8x + x2 = 7.343333333 Factor a perfect square on the left side: (x + 2.9)(x + 2.9) = 7.343333333 Calculate the square root of the right side: 2.709858545 Break this problem into two subproblems by setting (x + 2.9) equal to 2.709858545 and -2.709858545.Subproblem 1
x + 2.9 = 2.709858545 Simplifying x + 2.9 = 2.709858545 Reorder the terms: 2.9 + x = 2.709858545 Solving 2.9 + x = 2.709858545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + x = 2.709858545 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = 2.709858545 + -2.9 x = 2.709858545 + -2.9 Combine like terms: 2.709858545 + -2.9 = -0.190141455 x = -0.190141455 Simplifying x = -0.190141455Subproblem 2
x + 2.9 = -2.709858545 Simplifying x + 2.9 = -2.709858545 Reorder the terms: 2.9 + x = -2.709858545 Solving 2.9 + x = -2.709858545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + x = -2.709858545 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + x = -2.709858545 + -2.9 x = -2.709858545 + -2.9 Combine like terms: -2.709858545 + -2.9 = -5.609858545 x = -5.609858545 Simplifying x = -5.609858545Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.190141455, -5.609858545}
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