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Simplifying 3x2 + 31x + -18 = 0 Reorder the terms: -18 + 31x + 3x2 = 0 Solving -18 + 31x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 10.33333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 10.33333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 10.33333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 10.33333333x + x2 = 0 + 6 10.33333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 10.33333333x + x2 = 6 The x term is 10.33333333x. Take half its coefficient (5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. 10.33333333x + 26.69444443 + x2 = 6 + 26.69444443 Reorder the terms: 26.69444443 + 10.33333333x + x2 = 6 + 26.69444443 Combine like terms: 6 + 26.69444443 = 32.69444443 26.69444443 + 10.33333333x + x2 = 32.69444443 Factor a perfect square on the left side: (x + 5.166666665)(x + 5.166666665) = 32.69444443 Calculate the square root of the right side: 5.717905598 Break this problem into two subproblems by setting (x + 5.166666665) equal to 5.717905598 and -5.717905598.Subproblem 1
x + 5.166666665 = 5.717905598 Simplifying x + 5.166666665 = 5.717905598 Reorder the terms: 5.166666665 + x = 5.717905598 Solving 5.166666665 + x = 5.717905598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = 5.717905598 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = 5.717905598 + -5.166666665 x = 5.717905598 + -5.166666665 Combine like terms: 5.717905598 + -5.166666665 = 0.551238933 x = 0.551238933 Simplifying x = 0.551238933Subproblem 2
x + 5.166666665 = -5.717905598 Simplifying x + 5.166666665 = -5.717905598 Reorder the terms: 5.166666665 + x = -5.717905598 Solving 5.166666665 + x = -5.717905598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = -5.717905598 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = -5.717905598 + -5.166666665 x = -5.717905598 + -5.166666665 Combine like terms: -5.717905598 + -5.166666665 = -10.884572263 x = -10.884572263 Simplifying x = -10.884572263Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.551238933, -10.884572263}
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