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Simplifying 27x2 = 354x + 72 Reorder the terms: 27x2 = 72 + 354x Solving 27x2 = 72 + 354x Solving for variable 'x'. Reorder the terms: -72 + -354x + 27x2 = 72 + 354x + -72 + -354x Reorder the terms: -72 + -354x + 27x2 = 72 + -72 + 354x + -354x Combine like terms: 72 + -72 = 0 -72 + -354x + 27x2 = 0 + 354x + -354x -72 + -354x + 27x2 = 354x + -354x Combine like terms: 354x + -354x = 0 -72 + -354x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + -118x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + -118x + 9x2)' equal to zero and attempt to solve: Simplifying -24 + -118x + 9x2 = 0 Solving -24 + -118x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.666666667 + -13.11111111x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -13.11111111x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -13.11111111x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -13.11111111x + x2 = 0 + 2.666666667 -13.11111111x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -13.11111111x + x2 = 2.666666667 The x term is -13.11111111x. Take half its coefficient (-6.555555555). Square it (42.97530863) and add it to both sides. Add '42.97530863' to each side of the equation. -13.11111111x + 42.97530863 + x2 = 2.666666667 + 42.97530863 Reorder the terms: 42.97530863 + -13.11111111x + x2 = 2.666666667 + 42.97530863 Combine like terms: 2.666666667 + 42.97530863 = 45.641975297 42.97530863 + -13.11111111x + x2 = 45.641975297 Factor a perfect square on the left side: (x + -6.555555555)(x + -6.555555555) = 45.641975297 Calculate the square root of the right side: 6.755884494 Break this problem into two subproblems by setting (x + -6.555555555) equal to 6.755884494 and -6.755884494.Subproblem 1
x + -6.555555555 = 6.755884494 Simplifying x + -6.555555555 = 6.755884494 Reorder the terms: -6.555555555 + x = 6.755884494 Solving -6.555555555 + x = 6.755884494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.555555555' to each side of the equation. -6.555555555 + 6.555555555 + x = 6.755884494 + 6.555555555 Combine like terms: -6.555555555 + 6.555555555 = 0.000000000 0.000000000 + x = 6.755884494 + 6.555555555 x = 6.755884494 + 6.555555555 Combine like terms: 6.755884494 + 6.555555555 = 13.311440049 x = 13.311440049 Simplifying x = 13.311440049Subproblem 2
x + -6.555555555 = -6.755884494 Simplifying x + -6.555555555 = -6.755884494 Reorder the terms: -6.555555555 + x = -6.755884494 Solving -6.555555555 + x = -6.755884494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.555555555' to each side of the equation. -6.555555555 + 6.555555555 + x = -6.755884494 + 6.555555555 Combine like terms: -6.555555555 + 6.555555555 = 0.000000000 0.000000000 + x = -6.755884494 + 6.555555555 x = -6.755884494 + 6.555555555 Combine like terms: -6.755884494 + 6.555555555 = -0.200328939 x = -0.200328939 Simplifying x = -0.200328939Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.311440049, -0.200328939}Solution
x = {13.311440049, -0.200328939}
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