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Simplifying 2x2 + 38x + 113 = 0 Reorder the terms: 113 + 38x + 2x2 = 0 Solving 113 + 38x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 56.5 + 19x + x2 = 0 Move the constant term to the right: Add '-56.5' to each side of the equation. 56.5 + 19x + -56.5 + x2 = 0 + -56.5 Reorder the terms: 56.5 + -56.5 + 19x + x2 = 0 + -56.5 Combine like terms: 56.5 + -56.5 = 0.0 0.0 + 19x + x2 = 0 + -56.5 19x + x2 = 0 + -56.5 Combine like terms: 0 + -56.5 = -56.5 19x + x2 = -56.5 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -56.5 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -56.5 + 90.25 Combine like terms: -56.5 + 90.25 = 33.75 90.25 + 19x + x2 = 33.75 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 33.75 Calculate the square root of the right side: 5.809475019 Break this problem into two subproblems by setting (x + 9.5) equal to 5.809475019 and -5.809475019.Subproblem 1
x + 9.5 = 5.809475019 Simplifying x + 9.5 = 5.809475019 Reorder the terms: 9.5 + x = 5.809475019 Solving 9.5 + x = 5.809475019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 5.809475019 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 5.809475019 + -9.5 x = 5.809475019 + -9.5 Combine like terms: 5.809475019 + -9.5 = -3.690524981 x = -3.690524981 Simplifying x = -3.690524981Subproblem 2
x + 9.5 = -5.809475019 Simplifying x + 9.5 = -5.809475019 Reorder the terms: 9.5 + x = -5.809475019 Solving 9.5 + x = -5.809475019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -5.809475019 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -5.809475019 + -9.5 x = -5.809475019 + -9.5 Combine like terms: -5.809475019 + -9.5 = -15.309475019 x = -15.309475019 Simplifying x = -15.309475019Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.690524981, -15.309475019}
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