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Simplifying 8x + -1(2 + 6x) * 2(5 + -2x) = 126 Reorder the terms for easier multiplication: 8x + -1 * 2(2 + 6x)(5 + -2x) = 126 Multiply -1 * 2 8x + -2(2 + 6x)(5 + -2x) = 126 Multiply (2 + 6x) * (5 + -2x) 8x + -2(2(5 + -2x) + 6x * (5 + -2x)) = 126 8x + -2((5 * 2 + -2x * 2) + 6x * (5 + -2x)) = 126 8x + -2((10 + -4x) + 6x * (5 + -2x)) = 126 8x + -2(10 + -4x + (5 * 6x + -2x * 6x)) = 126 8x + -2(10 + -4x + (30x + -12x2)) = 126 Combine like terms: -4x + 30x = 26x 8x + -2(10 + 26x + -12x2) = 126 8x + (10 * -2 + 26x * -2 + -12x2 * -2) = 126 8x + (-20 + -52x + 24x2) = 126 Reorder the terms: -20 + 8x + -52x + 24x2 = 126 Combine like terms: 8x + -52x = -44x -20 + -44x + 24x2 = 126 Solving -20 + -44x + 24x2 = 126 Solving for variable 'x'. Reorder the terms: -20 + -126 + -44x + 24x2 = 126 + -126 Combine like terms: -20 + -126 = -146 -146 + -44x + 24x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -146 + -44x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-73 + -22x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-73 + -22x + 12x2)' equal to zero and attempt to solve: Simplifying -73 + -22x + 12x2 = 0 Solving -73 + -22x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -6.083333333 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '6.083333333' to each side of the equation. -6.083333333 + -1.833333333x + 6.083333333 + x2 = 0 + 6.083333333 Reorder the terms: -6.083333333 + 6.083333333 + -1.833333333x + x2 = 0 + 6.083333333 Combine like terms: -6.083333333 + 6.083333333 = 0.000000000 0.000000000 + -1.833333333x + x2 = 0 + 6.083333333 -1.833333333x + x2 = 0 + 6.083333333 Combine like terms: 0 + 6.083333333 = 6.083333333 -1.833333333x + x2 = 6.083333333 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = 6.083333333 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 6.083333333 + 0.8402777775 Combine like terms: 6.083333333 + 0.8402777775 = 6.9236111105 0.8402777775 + -1.833333333x + x2 = 6.9236111105 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 6.9236111105 Calculate the square root of the right side: 2.631275567 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 2.631275567 and -2.631275567.Subproblem 1
x + -0.9166666665 = 2.631275567 Simplifying x + -0.9166666665 = 2.631275567 Reorder the terms: -0.9166666665 + x = 2.631275567 Solving -0.9166666665 + x = 2.631275567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 2.631275567 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 2.631275567 + 0.9166666665 x = 2.631275567 + 0.9166666665 Combine like terms: 2.631275567 + 0.9166666665 = 3.5479422335 x = 3.5479422335 Simplifying x = 3.5479422335Subproblem 2
x + -0.9166666665 = -2.631275567 Simplifying x + -0.9166666665 = -2.631275567 Reorder the terms: -0.9166666665 + x = -2.631275567 Solving -0.9166666665 + x = -2.631275567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -2.631275567 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -2.631275567 + 0.9166666665 x = -2.631275567 + 0.9166666665 Combine like terms: -2.631275567 + 0.9166666665 = -1.7146089005 x = -1.7146089005 Simplifying x = -1.7146089005Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5479422335, -1.7146089005}Solution
x = {3.5479422335, -1.7146089005}
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