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Simplifying (9 + -8x)(8x + 9) + -72 = x(4 + -60) Reorder the terms: (9 + -8x)(9 + 8x) + -72 = x(4 + -60) Multiply (9 + -8x) * (9 + 8x) (9(9 + 8x) + -8x * (9 + 8x)) + -72 = x(4 + -60) ((9 * 9 + 8x * 9) + -8x * (9 + 8x)) + -72 = x(4 + -60) ((81 + 72x) + -8x * (9 + 8x)) + -72 = x(4 + -60) (81 + 72x + (9 * -8x + 8x * -8x)) + -72 = x(4 + -60) (81 + 72x + (-72x + -64x2)) + -72 = x(4 + -60) Combine like terms: 72x + -72x = 0 (81 + 0 + -64x2) + -72 = x(4 + -60) (81 + -64x2) + -72 = x(4 + -60) Reorder the terms: 81 + -72 + -64x2 = x(4 + -60) Combine like terms: 81 + -72 = 9 9 + -64x2 = x(4 + -60) Combine like terms: 4 + -60 = -56 9 + -64x2 = x(-56) Reorder the terms for easier multiplication: 9 + -64x2 = -56x Solving 9 + -64x2 = -56x Solving for variable 'x'. Reorder the terms: 9 + 56x + -64x2 = -56x + 56x Combine like terms: -56x + 56x = 0 9 + 56x + -64x2 = 0 Begin completing the square. Divide all terms by -64 the coefficient of the squared term: Divide each side by '-64'. -0.140625 + -0.875x + x2 = 0 Move the constant term to the right: Add '0.140625' to each side of the equation. -0.140625 + -0.875x + 0.140625 + x2 = 0 + 0.140625 Reorder the terms: -0.140625 + 0.140625 + -0.875x + x2 = 0 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + -0.875x + x2 = 0 + 0.140625 -0.875x + x2 = 0 + 0.140625 Combine like terms: 0 + 0.140625 = 0.140625 -0.875x + x2 = 0.140625 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 0.140625 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 0.140625 + 0.19140625 Combine like terms: 0.140625 + 0.19140625 = 0.33203125 0.19140625 + -0.875x + x2 = 0.33203125 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 0.33203125 Calculate the square root of the right side: 0.576221529 Break this problem into two subproblems by setting (x + -0.4375) equal to 0.576221529 and -0.576221529.Subproblem 1
x + -0.4375 = 0.576221529 Simplifying x + -0.4375 = 0.576221529 Reorder the terms: -0.4375 + x = 0.576221529 Solving -0.4375 + x = 0.576221529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 0.576221529 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 0.576221529 + 0.4375 x = 0.576221529 + 0.4375 Combine like terms: 0.576221529 + 0.4375 = 1.013721529 x = 1.013721529 Simplifying x = 1.013721529Subproblem 2
x + -0.4375 = -0.576221529 Simplifying x + -0.4375 = -0.576221529 Reorder the terms: -0.4375 + x = -0.576221529 Solving -0.4375 + x = -0.576221529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -0.576221529 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -0.576221529 + 0.4375 x = -0.576221529 + 0.4375 Combine like terms: -0.576221529 + 0.4375 = -0.138721529 x = -0.138721529 Simplifying x = -0.138721529Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.013721529, -0.138721529}
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