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Simplifying (5x + -18)(4x + 45) = 180 Reorder the terms: (-18 + 5x)(4x + 45) = 180 Reorder the terms: (-18 + 5x)(45 + 4x) = 180 Multiply (-18 + 5x) * (45 + 4x) (-18(45 + 4x) + 5x * (45 + 4x)) = 180 ((45 * -18 + 4x * -18) + 5x * (45 + 4x)) = 180 ((-810 + -72x) + 5x * (45 + 4x)) = 180 (-810 + -72x + (45 * 5x + 4x * 5x)) = 180 (-810 + -72x + (225x + 20x2)) = 180 Combine like terms: -72x + 225x = 153x (-810 + 153x + 20x2) = 180 Solving -810 + 153x + 20x2 = 180 Solving for variable 'x'. Reorder the terms: -810 + -180 + 153x + 20x2 = 180 + -180 Combine like terms: -810 + -180 = -990 -990 + 153x + 20x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -990 + 153x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -49.5 + 7.65x + x2 = 0.0 Move the constant term to the right: Add '49.5' to each side of the equation. -49.5 + 7.65x + 49.5 + x2 = 0.0 + 49.5 Reorder the terms: -49.5 + 49.5 + 7.65x + x2 = 0.0 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + 7.65x + x2 = 0.0 + 49.5 7.65x + x2 = 0.0 + 49.5 Combine like terms: 0.0 + 49.5 = 49.5 7.65x + x2 = 49.5 The x term is 7.65x. Take half its coefficient (3.825). Square it (14.630625) and add it to both sides. Add '14.630625' to each side of the equation. 7.65x + 14.630625 + x2 = 49.5 + 14.630625 Reorder the terms: 14.630625 + 7.65x + x2 = 49.5 + 14.630625 Combine like terms: 49.5 + 14.630625 = 64.130625 14.630625 + 7.65x + x2 = 64.130625 Factor a perfect square on the left side: (x + 3.825)(x + 3.825) = 64.130625 Calculate the square root of the right side: 8.008159901 Break this problem into two subproblems by setting (x + 3.825) equal to 8.008159901 and -8.008159901.Subproblem 1
x + 3.825 = 8.008159901 Simplifying x + 3.825 = 8.008159901 Reorder the terms: 3.825 + x = 8.008159901 Solving 3.825 + x = 8.008159901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.825' to each side of the equation. 3.825 + -3.825 + x = 8.008159901 + -3.825 Combine like terms: 3.825 + -3.825 = 0.000 0.000 + x = 8.008159901 + -3.825 x = 8.008159901 + -3.825 Combine like terms: 8.008159901 + -3.825 = 4.183159901 x = 4.183159901 Simplifying x = 4.183159901Subproblem 2
x + 3.825 = -8.008159901 Simplifying x + 3.825 = -8.008159901 Reorder the terms: 3.825 + x = -8.008159901 Solving 3.825 + x = -8.008159901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.825' to each side of the equation. 3.825 + -3.825 + x = -8.008159901 + -3.825 Combine like terms: 3.825 + -3.825 = 0.000 0.000 + x = -8.008159901 + -3.825 x = -8.008159901 + -3.825 Combine like terms: -8.008159901 + -3.825 = -11.833159901 x = -11.833159901 Simplifying x = -11.833159901Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.183159901, -11.833159901}
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