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Simplifying -3x * x + -31x + -6 = 0 Multiply x * x -3x2 + -31x + -6 = 0 Reorder the terms: -6 + -31x + -3x2 = 0 Solving -6 + -31x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 31x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 31x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + 31x + 3x2 = 0 Solving 6 + 31x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + 10.33333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 10.33333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 10.33333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 10.33333333x + x2 = 0 + -2 10.33333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 10.33333333x + x2 = -2 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 = -2 + 26.69444443 Reorder the terms: 26.69444443 + 10.33333333x + x2 = -2 + 26.69444443 Combine like terms: -2 + 26.69444443 = 24.69444443 26.69444443 + 10.33333333x + x2 = 24.69444443 Factor a perfect square on the left side: (x + 5.166666665)(x + 5.166666665) = 24.69444443 Calculate the square root of the right side: 4.969350504 Break this problem into two subproblems by setting (x + 5.166666665) equal to 4.969350504 and -4.969350504.Subproblem 1
x + 5.166666665 = 4.969350504 Simplifying x + 5.166666665 = 4.969350504 Reorder the terms: 5.166666665 + x = 4.969350504 Solving 5.166666665 + x = 4.969350504 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 = 4.969350504 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = 4.969350504 + -5.166666665 x = 4.969350504 + -5.166666665 Combine like terms: 4.969350504 + -5.166666665 = -0.197316161 x = -0.197316161 Simplifying x = -0.197316161Subproblem 2
x + 5.166666665 = -4.969350504 Simplifying x + 5.166666665 = -4.969350504 Reorder the terms: 5.166666665 + x = -4.969350504 Solving 5.166666665 + x = -4.969350504 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 = -4.969350504 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = -4.969350504 + -5.166666665 x = -4.969350504 + -5.166666665 Combine like terms: -4.969350504 + -5.166666665 = -10.136017169 x = -10.136017169 Simplifying x = -10.136017169Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.197316161, -10.136017169}Solution
x = {-0.197316161, -10.136017169}
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