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Simplifying (13x + 8)(5x + -8) = 180 Reorder the terms: (8 + 13x)(5x + -8) = 180 Reorder the terms: (8 + 13x)(-8 + 5x) = 180 Multiply (8 + 13x) * (-8 + 5x) (8(-8 + 5x) + 13x * (-8 + 5x)) = 180 ((-8 * 8 + 5x * 8) + 13x * (-8 + 5x)) = 180 ((-64 + 40x) + 13x * (-8 + 5x)) = 180 (-64 + 40x + (-8 * 13x + 5x * 13x)) = 180 (-64 + 40x + (-104x + 65x2)) = 180 Combine like terms: 40x + -104x = -64x (-64 + -64x + 65x2) = 180 Solving -64 + -64x + 65x2 = 180 Solving for variable 'x'. Reorder the terms: -64 + -180 + -64x + 65x2 = 180 + -180 Combine like terms: -64 + -180 = -244 -244 + -64x + 65x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -244 + -64x + 65x2 = 0 Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. -3.753846154 + -0.9846153846x + x2 = 0 Move the constant term to the right: Add '3.753846154' to each side of the equation. -3.753846154 + -0.9846153846x + 3.753846154 + x2 = 0 + 3.753846154 Reorder the terms: -3.753846154 + 3.753846154 + -0.9846153846x + x2 = 0 + 3.753846154 Combine like terms: -3.753846154 + 3.753846154 = 0.000000000 0.000000000 + -0.9846153846x + x2 = 0 + 3.753846154 -0.9846153846x + x2 = 0 + 3.753846154 Combine like terms: 0 + 3.753846154 = 3.753846154 -0.9846153846x + x2 = 3.753846154 The x term is -0.9846153846x. Take half its coefficient (-0.4923076923). Square it (0.2423668639) and add it to both sides. Add '0.2423668639' to each side of the equation. -0.9846153846x + 0.2423668639 + x2 = 3.753846154 + 0.2423668639 Reorder the terms: 0.2423668639 + -0.9846153846x + x2 = 3.753846154 + 0.2423668639 Combine like terms: 3.753846154 + 0.2423668639 = 3.9962130179 0.2423668639 + -0.9846153846x + x2 = 3.9962130179 Factor a perfect square on the left side: (x + -0.4923076923)(x + -0.4923076923) = 3.9962130179 Calculate the square root of the right side: 1.99905303 Break this problem into two subproblems by setting (x + -0.4923076923) equal to 1.99905303 and -1.99905303.Subproblem 1
x + -0.4923076923 = 1.99905303 Simplifying x + -0.4923076923 = 1.99905303 Reorder the terms: -0.4923076923 + x = 1.99905303 Solving -0.4923076923 + x = 1.99905303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4923076923' to each side of the equation. -0.4923076923 + 0.4923076923 + x = 1.99905303 + 0.4923076923 Combine like terms: -0.4923076923 + 0.4923076923 = 0.0000000000 0.0000000000 + x = 1.99905303 + 0.4923076923 x = 1.99905303 + 0.4923076923 Combine like terms: 1.99905303 + 0.4923076923 = 2.4913607223 x = 2.4913607223 Simplifying x = 2.4913607223Subproblem 2
x + -0.4923076923 = -1.99905303 Simplifying x + -0.4923076923 = -1.99905303 Reorder the terms: -0.4923076923 + x = -1.99905303 Solving -0.4923076923 + x = -1.99905303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4923076923' to each side of the equation. -0.4923076923 + 0.4923076923 + x = -1.99905303 + 0.4923076923 Combine like terms: -0.4923076923 + 0.4923076923 = 0.0000000000 0.0000000000 + x = -1.99905303 + 0.4923076923 x = -1.99905303 + 0.4923076923 Combine like terms: -1.99905303 + 0.4923076923 = -1.5067453377 x = -1.5067453377 Simplifying x = -1.5067453377Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4913607223, -1.5067453377}
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