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Simplifying 6x2 + -2x + -108 = 0 Reorder the terms: -108 + -2x + 6x2 = 0 Solving -108 + -2x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + -1x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -54 + -1x + 3x2 = 0 Solving -54 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -0.3333333333x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -0.3333333333x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -0.3333333333x + x2 = 0 + 18 -0.3333333333x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -0.3333333333x + x2 = 18 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 18 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 18 + 0.02777777779 Combine like terms: 18 + 0.02777777779 = 18.02777777779 0.02777777779 + -0.3333333333x + x2 = 18.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 18.02777777779 Calculate the square root of the right side: 4.245913068 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 4.245913068 and -4.245913068.Subproblem 1
x + -0.1666666667 = 4.245913068 Simplifying x + -0.1666666667 = 4.245913068 Reorder the terms: -0.1666666667 + x = 4.245913068 Solving -0.1666666667 + x = 4.245913068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 4.245913068 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 4.245913068 + 0.1666666667 x = 4.245913068 + 0.1666666667 Combine like terms: 4.245913068 + 0.1666666667 = 4.4125797347 x = 4.4125797347 Simplifying x = 4.4125797347Subproblem 2
x + -0.1666666667 = -4.245913068 Simplifying x + -0.1666666667 = -4.245913068 Reorder the terms: -0.1666666667 + x = -4.245913068 Solving -0.1666666667 + x = -4.245913068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -4.245913068 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -4.245913068 + 0.1666666667 x = -4.245913068 + 0.1666666667 Combine like terms: -4.245913068 + 0.1666666667 = -4.0792464013 x = -4.0792464013 Simplifying x = -4.0792464013Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4125797347, -4.0792464013}Solution
x = {4.4125797347, -4.0792464013}
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