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Simplifying -6x2 + 110x + -210 = 0 Reorder the terms: -210 + 110x + -6x2 = 0 Solving -210 + 110x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + 55x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-105 + 55x + -3x2)' equal to zero and attempt to solve: Simplifying -105 + 55x + -3x2 = 0 Solving -105 + 55x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 35 + -18.33333333x + x2 = 0 Move the constant term to the right: Add '-35' to each side of the equation. 35 + -18.33333333x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -18.33333333x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -18.33333333x + x2 = 0 + -35 -18.33333333x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -18.33333333x + x2 = -35 The x term is -18.33333333x. Take half its coefficient (-9.166666665). Square it (84.02777775) and add it to both sides. Add '84.02777775' to each side of the equation. -18.33333333x + 84.02777775 + x2 = -35 + 84.02777775 Reorder the terms: 84.02777775 + -18.33333333x + x2 = -35 + 84.02777775 Combine like terms: -35 + 84.02777775 = 49.02777775 84.02777775 + -18.33333333x + x2 = 49.02777775 Factor a perfect square on the left side: (x + -9.166666665)(x + -9.166666665) = 49.02777775 Calculate the square root of the right side: 7.001983844 Break this problem into two subproblems by setting (x + -9.166666665) equal to 7.001983844 and -7.001983844.Subproblem 1
x + -9.166666665 = 7.001983844 Simplifying x + -9.166666665 = 7.001983844 Reorder the terms: -9.166666665 + x = 7.001983844 Solving -9.166666665 + x = 7.001983844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.166666665' to each side of the equation. -9.166666665 + 9.166666665 + x = 7.001983844 + 9.166666665 Combine like terms: -9.166666665 + 9.166666665 = 0.000000000 0.000000000 + x = 7.001983844 + 9.166666665 x = 7.001983844 + 9.166666665 Combine like terms: 7.001983844 + 9.166666665 = 16.168650509 x = 16.168650509 Simplifying x = 16.168650509Subproblem 2
x + -9.166666665 = -7.001983844 Simplifying x + -9.166666665 = -7.001983844 Reorder the terms: -9.166666665 + x = -7.001983844 Solving -9.166666665 + x = -7.001983844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.166666665' to each side of the equation. -9.166666665 + 9.166666665 + x = -7.001983844 + 9.166666665 Combine like terms: -9.166666665 + 9.166666665 = 0.000000000 0.000000000 + x = -7.001983844 + 9.166666665 x = -7.001983844 + 9.166666665 Combine like terms: -7.001983844 + 9.166666665 = 2.164682821 x = 2.164682821 Simplifying x = 2.164682821Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.168650509, 2.164682821}Solution
x = {16.168650509, 2.164682821}
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