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Simplifying 8x(x + 13) = 9(-2x + -1) Reorder the terms: 8x(13 + x) = 9(-2x + -1) (13 * 8x + x * 8x) = 9(-2x + -1) (104x + 8x2) = 9(-2x + -1) Reorder the terms: 104x + 8x2 = 9(-1 + -2x) 104x + 8x2 = (-1 * 9 + -2x * 9) 104x + 8x2 = (-9 + -18x) Solving 104x + 8x2 = -9 + -18x Solving for variable 'x'. Reorder the terms: 9 + 104x + 18x + 8x2 = -9 + -18x + 9 + 18x Combine like terms: 104x + 18x = 122x 9 + 122x + 8x2 = -9 + -18x + 9 + 18x Reorder the terms: 9 + 122x + 8x2 = -9 + 9 + -18x + 18x Combine like terms: -9 + 9 = 0 9 + 122x + 8x2 = 0 + -18x + 18x 9 + 122x + 8x2 = -18x + 18x Combine like terms: -18x + 18x = 0 9 + 122x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + 15.25x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 15.25x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 15.25x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 15.25x + x2 = 0 + -1.125 15.25x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 15.25x + x2 = -1.125 The x term is 15.25x. Take half its coefficient (7.625). Square it (58.140625) and add it to both sides. Add '58.140625' to each side of the equation. 15.25x + 58.140625 + x2 = -1.125 + 58.140625 Reorder the terms: 58.140625 + 15.25x + x2 = -1.125 + 58.140625 Combine like terms: -1.125 + 58.140625 = 57.015625 58.140625 + 15.25x + x2 = 57.015625 Factor a perfect square on the left side: (x + 7.625)(x + 7.625) = 57.015625 Calculate the square root of the right side: 7.550869155 Break this problem into two subproblems by setting (x + 7.625) equal to 7.550869155 and -7.550869155.Subproblem 1
x + 7.625 = 7.550869155 Simplifying x + 7.625 = 7.550869155 Reorder the terms: 7.625 + x = 7.550869155 Solving 7.625 + x = 7.550869155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.625' to each side of the equation. 7.625 + -7.625 + x = 7.550869155 + -7.625 Combine like terms: 7.625 + -7.625 = 0.000 0.000 + x = 7.550869155 + -7.625 x = 7.550869155 + -7.625 Combine like terms: 7.550869155 + -7.625 = -0.074130845 x = -0.074130845 Simplifying x = -0.074130845Subproblem 2
x + 7.625 = -7.550869155 Simplifying x + 7.625 = -7.550869155 Reorder the terms: 7.625 + x = -7.550869155 Solving 7.625 + x = -7.550869155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.625' to each side of the equation. 7.625 + -7.625 + x = -7.550869155 + -7.625 Combine like terms: 7.625 + -7.625 = 0.000 0.000 + x = -7.550869155 + -7.625 x = -7.550869155 + -7.625 Combine like terms: -7.550869155 + -7.625 = -15.175869155 x = -15.175869155 Simplifying x = -15.175869155Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.074130845, -15.175869155}
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