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Simplifying 44(x + 20) * 3x = 180 Reorder the terms: 44(20 + x) * 3x = 180 Reorder the terms for easier multiplication: 44 * 3x(20 + x) = 180 Multiply 44 * 3 132x(20 + x) = 180 (20 * 132x + x * 132x) = 180 (2640x + 132x2) = 180 Solving 2640x + 132x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 2640x + 132x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 2640x + 132x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-15 + 220x + 11x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-15 + 220x + 11x2)' equal to zero and attempt to solve: Simplifying -15 + 220x + 11x2 = 0 Solving -15 + 220x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.363636364 + 20x + x2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + 20x + 1.363636364 + x2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + 20x + x2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + 20x + x2 = 0 + 1.363636364 20x + x2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 20x + x2 = 1.363636364 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 1.363636364 + 100 Reorder the terms: 100 + 20x + x2 = 1.363636364 + 100 Combine like terms: 1.363636364 + 100 = 101.363636364 100 + 20x + x2 = 101.363636364 Factor a perfect square on the left side: (x + 10)(x + 10) = 101.363636364 Calculate the square root of the right side: 10.067950952 Break this problem into two subproblems by setting (x + 10) equal to 10.067950952 and -10.067950952.Subproblem 1
x + 10 = 10.067950952 Simplifying x + 10 = 10.067950952 Reorder the terms: 10 + x = 10.067950952 Solving 10 + x = 10.067950952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.067950952 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.067950952 + -10 x = 10.067950952 + -10 Combine like terms: 10.067950952 + -10 = 0.067950952 x = 0.067950952 Simplifying x = 0.067950952Subproblem 2
x + 10 = -10.067950952 Simplifying x + 10 = -10.067950952 Reorder the terms: 10 + x = -10.067950952 Solving 10 + x = -10.067950952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.067950952 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.067950952 + -10 x = -10.067950952 + -10 Combine like terms: -10.067950952 + -10 = -20.067950952 x = -20.067950952 Simplifying x = -20.067950952Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.067950952, -20.067950952}Solution
x = {0.067950952, -20.067950952}
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