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Simplifying (3x + -20)(x + -20) = 120 Reorder the terms: (-20 + 3x)(x + -20) = 120 Reorder the terms: (-20 + 3x)(-20 + x) = 120 Multiply (-20 + 3x) * (-20 + x) (-20(-20 + x) + 3x * (-20 + x)) = 120 ((-20 * -20 + x * -20) + 3x * (-20 + x)) = 120 ((400 + -20x) + 3x * (-20 + x)) = 120 (400 + -20x + (-20 * 3x + x * 3x)) = 120 (400 + -20x + (-60x + 3x2)) = 120 Combine like terms: -20x + -60x = -80x (400 + -80x + 3x2) = 120 Solving 400 + -80x + 3x2 = 120 Solving for variable 'x'. Reorder the terms: 400 + -120 + -80x + 3x2 = 120 + -120 Combine like terms: 400 + -120 = 280 280 + -80x + 3x2 = 120 + -120 Combine like terms: 120 + -120 = 0 280 + -80x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 93.33333333 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '-93.33333333' to each side of the equation. 93.33333333 + -26.66666667x + -93.33333333 + x2 = 0 + -93.33333333 Reorder the terms: 93.33333333 + -93.33333333 + -26.66666667x + x2 = 0 + -93.33333333 Combine like terms: 93.33333333 + -93.33333333 = 0.00000000 0.00000000 + -26.66666667x + x2 = 0 + -93.33333333 -26.66666667x + x2 = 0 + -93.33333333 Combine like terms: 0 + -93.33333333 = -93.33333333 -26.66666667x + x2 = -93.33333333 The x term is -26.66666667x. Take half its coefficient (-13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. -26.66666667x + 177.7777780 + x2 = -93.33333333 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = -93.33333333 + 177.7777780 Combine like terms: -93.33333333 + 177.7777780 = 84.44444467 177.7777780 + -26.66666667x + x2 = 84.44444467 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 84.44444467 Calculate the square root of the right side: 9.189365847 Break this problem into two subproblems by setting (x + -13.33333334) equal to 9.189365847 and -9.189365847.Subproblem 1
x + -13.33333334 = 9.189365847 Simplifying x + -13.33333334 = 9.189365847 Reorder the terms: -13.33333334 + x = 9.189365847 Solving -13.33333334 + x = 9.189365847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = 9.189365847 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 9.189365847 + 13.33333334 x = 9.189365847 + 13.33333334 Combine like terms: 9.189365847 + 13.33333334 = 22.522699187 x = 22.522699187 Simplifying x = 22.522699187Subproblem 2
x + -13.33333334 = -9.189365847 Simplifying x + -13.33333334 = -9.189365847 Reorder the terms: -13.33333334 + x = -9.189365847 Solving -13.33333334 + x = -9.189365847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + x = -9.189365847 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -9.189365847 + 13.33333334 x = -9.189365847 + 13.33333334 Combine like terms: -9.189365847 + 13.33333334 = 4.143967493 x = 4.143967493 Simplifying x = 4.143967493Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.522699187, 4.143967493}
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