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Simplifying 6x2 + -74x + 171 = 0 Reorder the terms: 171 + -74x + 6x2 = 0 Solving 171 + -74x + 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'. 28.5 + -12.33333333x + x2 = 0 Move the constant term to the right: Add '-28.5' to each side of the equation. 28.5 + -12.33333333x + -28.5 + x2 = 0 + -28.5 Reorder the terms: 28.5 + -28.5 + -12.33333333x + x2 = 0 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + -12.33333333x + x2 = 0 + -28.5 -12.33333333x + x2 = 0 + -28.5 Combine like terms: 0 + -28.5 = -28.5 -12.33333333x + x2 = -28.5 The x term is -12.33333333x. Take half its coefficient (-6.166666665). Square it (38.02777776) and add it to both sides. Add '38.02777776' to each side of the equation. -12.33333333x + 38.02777776 + x2 = -28.5 + 38.02777776 Reorder the terms: 38.02777776 + -12.33333333x + x2 = -28.5 + 38.02777776 Combine like terms: -28.5 + 38.02777776 = 9.52777776 38.02777776 + -12.33333333x + x2 = 9.52777776 Factor a perfect square on the left side: (x + -6.166666665)(x + -6.166666665) = 9.52777776 Calculate the square root of the right side: 3.08670986 Break this problem into two subproblems by setting (x + -6.166666665) equal to 3.08670986 and -3.08670986.Subproblem 1
x + -6.166666665 = 3.08670986 Simplifying x + -6.166666665 = 3.08670986 Reorder the terms: -6.166666665 + x = 3.08670986 Solving -6.166666665 + x = 3.08670986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x = 3.08670986 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x = 3.08670986 + 6.166666665 x = 3.08670986 + 6.166666665 Combine like terms: 3.08670986 + 6.166666665 = 9.253376525 x = 9.253376525 Simplifying x = 9.253376525Subproblem 2
x + -6.166666665 = -3.08670986 Simplifying x + -6.166666665 = -3.08670986 Reorder the terms: -6.166666665 + x = -3.08670986 Solving -6.166666665 + x = -3.08670986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x = -3.08670986 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x = -3.08670986 + 6.166666665 x = -3.08670986 + 6.166666665 Combine like terms: -3.08670986 + 6.166666665 = 3.079956805 x = 3.079956805 Simplifying x = 3.079956805Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.253376525, 3.079956805}
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