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Simplifying 6x2 + 31x = 12 Reorder the terms: 31x + 6x2 = 12 Solving 31x + 6x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 31x + 6x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 31x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2 + 5.166666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 5.166666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 5.166666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5.166666667x + x2 = 0 + 2 5.166666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 5.166666667x + x2 = 2 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 = 2 + 6.673611115 Reorder the terms: 6.673611115 + 5.166666667x + x2 = 2 + 6.673611115 Combine like terms: 2 + 6.673611115 = 8.673611115 6.673611115 + 5.166666667x + x2 = 8.673611115 Factor a perfect square on the left side: (x + 2.583333334)(x + 2.583333334) = 8.673611115 Calculate the square root of the right side: 2.945099509 Break this problem into two subproblems by setting (x + 2.583333334) equal to 2.945099509 and -2.945099509.Subproblem 1
x + 2.583333334 = 2.945099509 Simplifying x + 2.583333334 = 2.945099509 Reorder the terms: 2.583333334 + x = 2.945099509 Solving 2.583333334 + x = 2.945099509 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 = 2.945099509 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = 2.945099509 + -2.583333334 x = 2.945099509 + -2.583333334 Combine like terms: 2.945099509 + -2.583333334 = 0.361766175 x = 0.361766175 Simplifying x = 0.361766175Subproblem 2
x + 2.583333334 = -2.945099509 Simplifying x + 2.583333334 = -2.945099509 Reorder the terms: 2.583333334 + x = -2.945099509 Solving 2.583333334 + x = -2.945099509 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 = -2.945099509 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = -2.945099509 + -2.583333334 x = -2.945099509 + -2.583333334 Combine like terms: -2.945099509 + -2.583333334 = -5.528432843 x = -5.528432843 Simplifying x = -5.528432843Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.361766175, -5.528432843}
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