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Simplifying (20x + 10)(3x + 9) = 180 Reorder the terms: (10 + 20x)(3x + 9) = 180 Reorder the terms: (10 + 20x)(9 + 3x) = 180 Multiply (10 + 20x) * (9 + 3x) (10(9 + 3x) + 20x * (9 + 3x)) = 180 ((9 * 10 + 3x * 10) + 20x * (9 + 3x)) = 180 ((90 + 30x) + 20x * (9 + 3x)) = 180 (90 + 30x + (9 * 20x + 3x * 20x)) = 180 (90 + 30x + (180x + 60x2)) = 180 Combine like terms: 30x + 180x = 210x (90 + 210x + 60x2) = 180 Solving 90 + 210x + 60x2 = 180 Solving for variable 'x'. Reorder the terms: 90 + -180 + 210x + 60x2 = 180 + -180 Combine like terms: 90 + -180 = -90 -90 + 210x + 60x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -90 + 210x + 60x2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(-3 + 7x + 2x2) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(-3 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + 7x + 2x2 = 0 Solving -3 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 3.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 3.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 3.5x + x2 = 0 + 1.5 3.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 3.5x + x2 = 1.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 1.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 1.5 + 3.0625 Combine like terms: 1.5 + 3.0625 = 4.5625 3.0625 + 3.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + 1.75) equal to 2.136000936 and -2.136000936.Subproblem 1
x + 1.75 = 2.136000936 Simplifying x + 1.75 = 2.136000936 Reorder the terms: 1.75 + x = 2.136000936 Solving 1.75 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.136000936 + -1.75 x = 2.136000936 + -1.75 Combine like terms: 2.136000936 + -1.75 = 0.386000936 x = 0.386000936 Simplifying x = 0.386000936Subproblem 2
x + 1.75 = -2.136000936 Simplifying x + 1.75 = -2.136000936 Reorder the terms: 1.75 + x = -2.136000936 Solving 1.75 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.136000936 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.136000936 + -1.75 x = -2.136000936 + -1.75 Combine like terms: -2.136000936 + -1.75 = -3.886000936 x = -3.886000936 Simplifying x = -3.886000936Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.386000936, -3.886000936}Solution
x = {0.386000936, -3.886000936}
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