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Simplifying (5x + 9)(8x + -15) = 180 Reorder the terms: (9 + 5x)(8x + -15) = 180 Reorder the terms: (9 + 5x)(-15 + 8x) = 180 Multiply (9 + 5x) * (-15 + 8x) (9(-15 + 8x) + 5x * (-15 + 8x)) = 180 ((-15 * 9 + 8x * 9) + 5x * (-15 + 8x)) = 180 ((-135 + 72x) + 5x * (-15 + 8x)) = 180 (-135 + 72x + (-15 * 5x + 8x * 5x)) = 180 (-135 + 72x + (-75x + 40x2)) = 180 Combine like terms: 72x + -75x = -3x (-135 + -3x + 40x2) = 180 Solving -135 + -3x + 40x2 = 180 Solving for variable 'x'. Reorder the terms: -135 + -180 + -3x + 40x2 = 180 + -180 Combine like terms: -135 + -180 = -315 -315 + -3x + 40x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -315 + -3x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -7.875 + -0.075x + x2 = 0.0 Move the constant term to the right: Add '7.875' to each side of the equation. -7.875 + -0.075x + 7.875 + x2 = 0.0 + 7.875 Reorder the terms: -7.875 + 7.875 + -0.075x + x2 = 0.0 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + -0.075x + x2 = 0.0 + 7.875 -0.075x + x2 = 0.0 + 7.875 Combine like terms: 0.0 + 7.875 = 7.875 -0.075x + x2 = 7.875 The x term is -0.075x. Take half its coefficient (-0.0375). Square it (0.00140625) and add it to both sides. Add '0.00140625' to each side of the equation. -0.075x + 0.00140625 + x2 = 7.875 + 0.00140625 Reorder the terms: 0.00140625 + -0.075x + x2 = 7.875 + 0.00140625 Combine like terms: 7.875 + 0.00140625 = 7.87640625 0.00140625 + -0.075x + x2 = 7.87640625 Factor a perfect square on the left side: (x + -0.0375)(x + -0.0375) = 7.87640625 Calculate the square root of the right side: 2.806493586 Break this problem into two subproblems by setting (x + -0.0375) equal to 2.806493586 and -2.806493586.Subproblem 1
x + -0.0375 = 2.806493586 Simplifying x + -0.0375 = 2.806493586 Reorder the terms: -0.0375 + x = 2.806493586 Solving -0.0375 + x = 2.806493586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0375' to each side of the equation. -0.0375 + 0.0375 + x = 2.806493586 + 0.0375 Combine like terms: -0.0375 + 0.0375 = 0.0000 0.0000 + x = 2.806493586 + 0.0375 x = 2.806493586 + 0.0375 Combine like terms: 2.806493586 + 0.0375 = 2.843993586 x = 2.843993586 Simplifying x = 2.843993586Subproblem 2
x + -0.0375 = -2.806493586 Simplifying x + -0.0375 = -2.806493586 Reorder the terms: -0.0375 + x = -2.806493586 Solving -0.0375 + x = -2.806493586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0375' to each side of the equation. -0.0375 + 0.0375 + x = -2.806493586 + 0.0375 Combine like terms: -0.0375 + 0.0375 = 0.0000 0.0000 + x = -2.806493586 + 0.0375 x = -2.806493586 + 0.0375 Combine like terms: -2.806493586 + 0.0375 = -2.768993586 x = -2.768993586 Simplifying x = -2.768993586Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.843993586, -2.768993586}
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