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Simplifying 6x2 + -6x + -37 = 0 Reorder the terms: -37 + -6x + 6x2 = 0 Solving -37 + -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'. -6.166666667 + -1x + x2 = 0 Move the constant term to the right: Add '6.166666667' to each side of the equation. -6.166666667 + -1x + 6.166666667 + x2 = 0 + 6.166666667 Reorder the terms: -6.166666667 + 6.166666667 + -1x + x2 = 0 + 6.166666667 Combine like terms: -6.166666667 + 6.166666667 = 0.000000000 0.000000000 + -1x + x2 = 0 + 6.166666667 -1x + x2 = 0 + 6.166666667 Combine like terms: 0 + 6.166666667 = 6.166666667 -1x + x2 = 6.166666667 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 = 6.166666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6.166666667 + 0.25 Combine like terms: 6.166666667 + 0.25 = 6.416666667 0.25 + -1x + x2 = 6.416666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6.416666667 Calculate the square root of the right side: 2.533114026 Break this problem into two subproblems by setting (x + -0.5) equal to 2.533114026 and -2.533114026.Subproblem 1
x + -0.5 = 2.533114026 Simplifying x + -0.5 = 2.533114026 Reorder the terms: -0.5 + x = 2.533114026 Solving -0.5 + x = 2.533114026 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 = 2.533114026 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.533114026 + 0.5 x = 2.533114026 + 0.5 Combine like terms: 2.533114026 + 0.5 = 3.033114026 x = 3.033114026 Simplifying x = 3.033114026Subproblem 2
x + -0.5 = -2.533114026 Simplifying x + -0.5 = -2.533114026 Reorder the terms: -0.5 + x = -2.533114026 Solving -0.5 + x = -2.533114026 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 = -2.533114026 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.533114026 + 0.5 x = -2.533114026 + 0.5 Combine like terms: -2.533114026 + 0.5 = -2.033114026 x = -2.033114026 Simplifying x = -2.033114026Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.033114026, -2.033114026}
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