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Simplifying (4x + 30)(5x + 10) = 180 Reorder the terms: (30 + 4x)(5x + 10) = 180 Reorder the terms: (30 + 4x)(10 + 5x) = 180 Multiply (30 + 4x) * (10 + 5x) (30(10 + 5x) + 4x * (10 + 5x)) = 180 ((10 * 30 + 5x * 30) + 4x * (10 + 5x)) = 180 ((300 + 150x) + 4x * (10 + 5x)) = 180 (300 + 150x + (10 * 4x + 5x * 4x)) = 180 (300 + 150x + (40x + 20x2)) = 180 Combine like terms: 150x + 40x = 190x (300 + 190x + 20x2) = 180 Solving 300 + 190x + 20x2 = 180 Solving for variable 'x'. Reorder the terms: 300 + -180 + 190x + 20x2 = 180 + -180 Combine like terms: 300 + -180 = 120 120 + 190x + 20x2 = 180 + -180 Combine like terms: 180 + -180 = 0 120 + 190x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(12 + 19x + 2x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(12 + 19x + 2x2)' equal to zero and attempt to solve: Simplifying 12 + 19x + 2x2 = 0 Solving 12 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6 + 9.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 9.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 9.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 9.5x + x2 = 0 + -6 9.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 9.5x + x2 = -6 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -6 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -6 + 22.5625 Combine like terms: -6 + 22.5625 = 16.5625 22.5625 + 9.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + 4.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + 4.75 = 4.069705149 Simplifying x + 4.75 = 4.069705149 Reorder the terms: 4.75 + x = 4.069705149 Solving 4.75 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 4.069705149 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 4.069705149 + -4.75 x = 4.069705149 + -4.75 Combine like terms: 4.069705149 + -4.75 = -0.680294851 x = -0.680294851 Simplifying x = -0.680294851Subproblem 2
x + 4.75 = -4.069705149 Simplifying x + 4.75 = -4.069705149 Reorder the terms: 4.75 + x = -4.069705149 Solving 4.75 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -4.069705149 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -4.069705149 + -4.75 x = -4.069705149 + -4.75 Combine like terms: -4.069705149 + -4.75 = -8.819705149 x = -8.819705149 Simplifying x = -8.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.680294851, -8.819705149}Solution
x = {-0.680294851, -8.819705149}
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