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Simplifying 6x2 + -31x + 6 = 0 Reorder the terms: 6 + -31x + 6x2 = 0 Solving 6 + -31x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1 + -5.166666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.166666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5.166666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.166666667x + x2 = 0 + -1 -5.166666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.166666667x + x2 = -1 The x term is -5.166666667x. Take half its coefficient (-2.583333334). Square it (6.673611115) and add it to both sides. Add '6.673611115' to each side of the equation. -5.166666667x + 6.673611115 + x2 = -1 + 6.673611115 Reorder the terms: 6.673611115 + -5.166666667x + x2 = -1 + 6.673611115 Combine like terms: -1 + 6.673611115 = 5.673611115 6.673611115 + -5.166666667x + x2 = 5.673611115 Factor a perfect square on the left side: (x + -2.583333334)(x + -2.583333334) = 5.673611115 Calculate the square root of the right side: 2.381934322 Break this problem into two subproblems by setting (x + -2.583333334) equal to 2.381934322 and -2.381934322.Subproblem 1
x + -2.583333334 = 2.381934322 Simplifying x + -2.583333334 = 2.381934322 Reorder the terms: -2.583333334 + x = 2.381934322 Solving -2.583333334 + x = 2.381934322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.583333334' to each side of the equation. -2.583333334 + 2.583333334 + x = 2.381934322 + 2.583333334 Combine like terms: -2.583333334 + 2.583333334 = 0.000000000 0.000000000 + x = 2.381934322 + 2.583333334 x = 2.381934322 + 2.583333334 Combine like terms: 2.381934322 + 2.583333334 = 4.965267656 x = 4.965267656 Simplifying x = 4.965267656Subproblem 2
x + -2.583333334 = -2.381934322 Simplifying x + -2.583333334 = -2.381934322 Reorder the terms: -2.583333334 + x = -2.381934322 Solving -2.583333334 + x = -2.381934322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.583333334' to each side of the equation. -2.583333334 + 2.583333334 + x = -2.381934322 + 2.583333334 Combine like terms: -2.583333334 + 2.583333334 = 0.000000000 0.000000000 + x = -2.381934322 + 2.583333334 x = -2.381934322 + 2.583333334 Combine like terms: -2.381934322 + 2.583333334 = 0.201399012 x = 0.201399012 Simplifying x = 0.201399012Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.965267656, 0.201399012}
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