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Simplifying (5x + -3)(2x + 1) = 180 Reorder the terms: (-3 + 5x)(2x + 1) = 180 Reorder the terms: (-3 + 5x)(1 + 2x) = 180 Multiply (-3 + 5x) * (1 + 2x) (-3(1 + 2x) + 5x * (1 + 2x)) = 180 ((1 * -3 + 2x * -3) + 5x * (1 + 2x)) = 180 ((-3 + -6x) + 5x * (1 + 2x)) = 180 (-3 + -6x + (1 * 5x + 2x * 5x)) = 180 (-3 + -6x + (5x + 10x2)) = 180 Combine like terms: -6x + 5x = -1x (-3 + -1x + 10x2) = 180 Solving -3 + -1x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: -3 + -180 + -1x + 10x2 = 180 + -180 Combine like terms: -3 + -180 = -183 -183 + -1x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -183 + -1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -18.3 + -0.1x + x2 = 0.0 Move the constant term to the right: Add '18.3' to each side of the equation. -18.3 + -0.1x + 18.3 + x2 = 0.0 + 18.3 Reorder the terms: -18.3 + 18.3 + -0.1x + x2 = 0.0 + 18.3 Combine like terms: -18.3 + 18.3 = 0.0 0.0 + -0.1x + x2 = 0.0 + 18.3 -0.1x + x2 = 0.0 + 18.3 Combine like terms: 0.0 + 18.3 = 18.3 -0.1x + x2 = 18.3 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 18.3 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 18.3 + 0.0025 Combine like terms: 18.3 + 0.0025 = 18.3025 0.0025 + -0.1x + x2 = 18.3025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 18.3025 Calculate the square root of the right side: 4.27814212 Break this problem into two subproblems by setting (x + -0.05) equal to 4.27814212 and -4.27814212.Subproblem 1
x + -0.05 = 4.27814212 Simplifying x + -0.05 = 4.27814212 Reorder the terms: -0.05 + x = 4.27814212 Solving -0.05 + x = 4.27814212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 4.27814212 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 4.27814212 + 0.05 x = 4.27814212 + 0.05 Combine like terms: 4.27814212 + 0.05 = 4.32814212 x = 4.32814212 Simplifying x = 4.32814212Subproblem 2
x + -0.05 = -4.27814212 Simplifying x + -0.05 = -4.27814212 Reorder the terms: -0.05 + x = -4.27814212 Solving -0.05 + x = -4.27814212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -4.27814212 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -4.27814212 + 0.05 x = -4.27814212 + 0.05 Combine like terms: -4.27814212 + 0.05 = -4.22814212 x = -4.22814212 Simplifying x = -4.22814212Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.32814212, -4.22814212}
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