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Simplifying 27x2 + -48x + 15 = 0 Reorder the terms: 15 + -48x + 27x2 = 0 Solving 15 + -48x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -16x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -16x + 9x2)' equal to zero and attempt to solve: Simplifying 5 + -16x + 9x2 = 0 Solving 5 + -16x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -1.777777778x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -1.777777778x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -1.777777778x + x2 = 0 + -0.5555555556 -1.777777778x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -1.777777778x + x2 = -0.5555555556 The x term is -1.777777778x. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778x + 0.7901234570 + x2 = -0.5555555556 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = -0.5555555556 + 0.7901234570 Combine like terms: -0.5555555556 + 0.7901234570 = 0.2345679014 0.7901234570 + -1.777777778x + x2 = 0.2345679014 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 0.2345679014 Calculate the square root of the right side: 0.484322105 Break this problem into two subproblems by setting (x + -0.888888889) equal to 0.484322105 and -0.484322105.Subproblem 1
x + -0.888888889 = 0.484322105 Simplifying x + -0.888888889 = 0.484322105 Reorder the terms: -0.888888889 + x = 0.484322105 Solving -0.888888889 + x = 0.484322105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = 0.484322105 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 0.484322105 + 0.888888889 x = 0.484322105 + 0.888888889 Combine like terms: 0.484322105 + 0.888888889 = 1.373210994 x = 1.373210994 Simplifying x = 1.373210994Subproblem 2
x + -0.888888889 = -0.484322105 Simplifying x + -0.888888889 = -0.484322105 Reorder the terms: -0.888888889 + x = -0.484322105 Solving -0.888888889 + x = -0.484322105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = -0.484322105 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -0.484322105 + 0.888888889 x = -0.484322105 + 0.888888889 Combine like terms: -0.484322105 + 0.888888889 = 0.404566784 x = 0.404566784 Simplifying x = 0.404566784Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.373210994, 0.404566784}Solution
x = {1.373210994, 0.404566784}
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