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Simplifying (12 + -2x)(20 + -1x) = 126 Multiply (12 + -2x) * (20 + -1x) (12(20 + -1x) + -2x * (20 + -1x)) = 126 ((20 * 12 + -1x * 12) + -2x * (20 + -1x)) = 126 ((240 + -12x) + -2x * (20 + -1x)) = 126 (240 + -12x + (20 * -2x + -1x * -2x)) = 126 (240 + -12x + (-40x + 2x2)) = 126 Combine like terms: -12x + -40x = -52x (240 + -52x + 2x2) = 126 Solving 240 + -52x + 2x2 = 126 Solving for variable 'x'. Reorder the terms: 240 + -126 + -52x + 2x2 = 126 + -126 Combine like terms: 240 + -126 = 114 114 + -52x + 2x2 = 126 + -126 Combine like terms: 126 + -126 = 0 114 + -52x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(57 + -26x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(57 + -26x + x2)' equal to zero and attempt to solve: Simplifying 57 + -26x + x2 = 0 Solving 57 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + -26x + -57 + x2 = 0 + -57 Reorder the terms: 57 + -57 + -26x + x2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + -26x + x2 = 0 + -57 -26x + x2 = 0 + -57 Combine like terms: 0 + -57 = -57 -26x + x2 = -57 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -57 + 169 Reorder the terms: 169 + -26x + x2 = -57 + 169 Combine like terms: -57 + 169 = 112 169 + -26x + x2 = 112 Factor a perfect square on the left side: (x + -13)(x + -13) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + -13) equal to 10.583005244 and -10.583005244.Subproblem 1
x + -13 = 10.583005244 Simplifying x + -13 = 10.583005244 Reorder the terms: -13 + x = 10.583005244 Solving -13 + x = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 10.583005244 + 13 Combine like terms: -13 + 13 = 0 0 + x = 10.583005244 + 13 x = 10.583005244 + 13 Combine like terms: 10.583005244 + 13 = 23.583005244 x = 23.583005244 Simplifying x = 23.583005244Subproblem 2
x + -13 = -10.583005244 Simplifying x + -13 = -10.583005244 Reorder the terms: -13 + x = -10.583005244 Solving -13 + x = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -10.583005244 + 13 Combine like terms: -13 + 13 = 0 0 + x = -10.583005244 + 13 x = -10.583005244 + 13 Combine like terms: -10.583005244 + 13 = 2.416994756 x = 2.416994756 Simplifying x = 2.416994756Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.583005244, 2.416994756}Solution
x = {23.583005244, 2.416994756}
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