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Simplifying (8x + -5)(4x + -3) = 104 Reorder the terms: (-5 + 8x)(4x + -3) = 104 Reorder the terms: (-5 + 8x)(-3 + 4x) = 104 Multiply (-5 + 8x) * (-3 + 4x) (-5(-3 + 4x) + 8x * (-3 + 4x)) = 104 ((-3 * -5 + 4x * -5) + 8x * (-3 + 4x)) = 104 ((15 + -20x) + 8x * (-3 + 4x)) = 104 (15 + -20x + (-3 * 8x + 4x * 8x)) = 104 (15 + -20x + (-24x + 32x2)) = 104 Combine like terms: -20x + -24x = -44x (15 + -44x + 32x2) = 104 Solving 15 + -44x + 32x2 = 104 Solving for variable 'x'. Reorder the terms: 15 + -104 + -44x + 32x2 = 104 + -104 Combine like terms: 15 + -104 = -89 -89 + -44x + 32x2 = 104 + -104 Combine like terms: 104 + -104 = 0 -89 + -44x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -2.78125 + -1.375x + x2 = 0 Move the constant term to the right: Add '2.78125' to each side of the equation. -2.78125 + -1.375x + 2.78125 + x2 = 0 + 2.78125 Reorder the terms: -2.78125 + 2.78125 + -1.375x + x2 = 0 + 2.78125 Combine like terms: -2.78125 + 2.78125 = 0.00000 0.00000 + -1.375x + x2 = 0 + 2.78125 -1.375x + x2 = 0 + 2.78125 Combine like terms: 0 + 2.78125 = 2.78125 -1.375x + x2 = 2.78125 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = 2.78125 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 2.78125 + 0.47265625 Combine like terms: 2.78125 + 0.47265625 = 3.25390625 0.47265625 + -1.375x + x2 = 3.25390625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 3.25390625 Calculate the square root of the right side: 1.803858711 Break this problem into two subproblems by setting (x + -0.6875) equal to 1.803858711 and -1.803858711.Subproblem 1
x + -0.6875 = 1.803858711 Simplifying x + -0.6875 = 1.803858711 Reorder the terms: -0.6875 + x = 1.803858711 Solving -0.6875 + x = 1.803858711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 1.803858711 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 1.803858711 + 0.6875 x = 1.803858711 + 0.6875 Combine like terms: 1.803858711 + 0.6875 = 2.491358711 x = 2.491358711 Simplifying x = 2.491358711Subproblem 2
x + -0.6875 = -1.803858711 Simplifying x + -0.6875 = -1.803858711 Reorder the terms: -0.6875 + x = -1.803858711 Solving -0.6875 + x = -1.803858711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -1.803858711 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -1.803858711 + 0.6875 x = -1.803858711 + 0.6875 Combine like terms: -1.803858711 + 0.6875 = -1.116358711 x = -1.116358711 Simplifying x = -1.116358711Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.491358711, -1.116358711}
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