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Simplifying (8x + 1)(-5x + 9) = x Reorder the terms: (1 + 8x)(-5x + 9) = x Reorder the terms: (1 + 8x)(9 + -5x) = x Multiply (1 + 8x) * (9 + -5x) (1(9 + -5x) + 8x * (9 + -5x)) = x ((9 * 1 + -5x * 1) + 8x * (9 + -5x)) = x ((9 + -5x) + 8x * (9 + -5x)) = x (9 + -5x + (9 * 8x + -5x * 8x)) = x (9 + -5x + (72x + -40x2)) = x Combine like terms: -5x + 72x = 67x (9 + 67x + -40x2) = x Solving 9 + 67x + -40x2 = x Solving for variable 'x'. Reorder the terms: 9 + 67x + -1x + -40x2 = x + -1x Combine like terms: 67x + -1x = 66x 9 + 66x + -40x2 = x + -1x Combine like terms: x + -1x = 0 9 + 66x + -40x2 = 0 Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.225 + -1.65x + x2 = 0.0 Move the constant term to the right: Add '0.225' to each side of the equation. -0.225 + -1.65x + 0.225 + x2 = 0.0 + 0.225 Reorder the terms: -0.225 + 0.225 + -1.65x + x2 = 0.0 + 0.225 Combine like terms: -0.225 + 0.225 = 0.000 0.000 + -1.65x + x2 = 0.0 + 0.225 -1.65x + x2 = 0.0 + 0.225 Combine like terms: 0.0 + 0.225 = 0.225 -1.65x + x2 = 0.225 The x term is -1.65x. Take half its coefficient (-0.825). Square it (0.680625) and add it to both sides. Add '0.680625' to each side of the equation. -1.65x + 0.680625 + x2 = 0.225 + 0.680625 Reorder the terms: 0.680625 + -1.65x + x2 = 0.225 + 0.680625 Combine like terms: 0.225 + 0.680625 = 0.905625 0.680625 + -1.65x + x2 = 0.905625 Factor a perfect square on the left side: (x + -0.825)(x + -0.825) = 0.905625 Calculate the square root of the right side: 0.951643316 Break this problem into two subproblems by setting (x + -0.825) equal to 0.951643316 and -0.951643316.Subproblem 1
x + -0.825 = 0.951643316 Simplifying x + -0.825 = 0.951643316 Reorder the terms: -0.825 + x = 0.951643316 Solving -0.825 + x = 0.951643316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.825' to each side of the equation. -0.825 + 0.825 + x = 0.951643316 + 0.825 Combine like terms: -0.825 + 0.825 = 0.000 0.000 + x = 0.951643316 + 0.825 x = 0.951643316 + 0.825 Combine like terms: 0.951643316 + 0.825 = 1.776643316 x = 1.776643316 Simplifying x = 1.776643316Subproblem 2
x + -0.825 = -0.951643316 Simplifying x + -0.825 = -0.951643316 Reorder the terms: -0.825 + x = -0.951643316 Solving -0.825 + x = -0.951643316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.825' to each side of the equation. -0.825 + 0.825 + x = -0.951643316 + 0.825 Combine like terms: -0.825 + 0.825 = 0.000 0.000 + x = -0.951643316 + 0.825 x = -0.951643316 + 0.825 Combine like terms: -0.951643316 + 0.825 = -0.126643316 x = -0.126643316 Simplifying x = -0.126643316Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.776643316, -0.126643316}
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