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Simplifying 6x2 + -6x + -31 = 0 Reorder the terms: -31 + -6x + 6x2 = 0 Solving -31 + -6x + 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'. -5.166666667 + -1x + x2 = 0 Move the constant term to the right: Add '5.166666667' to each side of the equation. -5.166666667 + -1x + 5.166666667 + x2 = 0 + 5.166666667 Reorder the terms: -5.166666667 + 5.166666667 + -1x + x2 = 0 + 5.166666667 Combine like terms: -5.166666667 + 5.166666667 = 0.000000000 0.000000000 + -1x + x2 = 0 + 5.166666667 -1x + x2 = 0 + 5.166666667 Combine like terms: 0 + 5.166666667 = 5.166666667 -1x + x2 = 5.166666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 5.166666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5.166666667 + 0.25 Combine like terms: 5.166666667 + 0.25 = 5.416666667 0.25 + -1x + x2 = 5.416666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5.416666667 Calculate the square root of the right side: 2.327373341 Break this problem into two subproblems by setting (x + -0.5) equal to 2.327373341 and -2.327373341.Subproblem 1
x + -0.5 = 2.327373341 Simplifying x + -0.5 = 2.327373341 Reorder the terms: -0.5 + x = 2.327373341 Solving -0.5 + x = 2.327373341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.327373341 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.327373341 + 0.5 x = 2.327373341 + 0.5 Combine like terms: 2.327373341 + 0.5 = 2.827373341 x = 2.827373341 Simplifying x = 2.827373341Subproblem 2
x + -0.5 = -2.327373341 Simplifying x + -0.5 = -2.327373341 Reorder the terms: -0.5 + x = -2.327373341 Solving -0.5 + x = -2.327373341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.327373341 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.327373341 + 0.5 x = -2.327373341 + 0.5 Combine like terms: -2.327373341 + 0.5 = -1.827373341 x = -1.827373341 Simplifying x = -1.827373341Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.827373341, -1.827373341}
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