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Simplifying 9x2 + -151x + -14 = 0 Reorder the terms: -14 + -151x + 9x2 = 0 Solving -14 + -151x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + -16.77777778x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + -16.77777778x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + -16.77777778x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + -16.77777778x + x2 = 0 + 1.555555556 -16.77777778x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 -16.77777778x + x2 = 1.555555556 The x term is -16.77777778x. Take half its coefficient (-8.38888889). Square it (70.37345681) and add it to both sides. Add '70.37345681' to each side of the equation. -16.77777778x + 70.37345681 + x2 = 1.555555556 + 70.37345681 Reorder the terms: 70.37345681 + -16.77777778x + x2 = 1.555555556 + 70.37345681 Combine like terms: 1.555555556 + 70.37345681 = 71.929012366 70.37345681 + -16.77777778x + x2 = 71.929012366 Factor a perfect square on the left side: (x + -8.38888889)(x + -8.38888889) = 71.929012366 Calculate the square root of the right side: 8.481097356 Break this problem into two subproblems by setting (x + -8.38888889) equal to 8.481097356 and -8.481097356.Subproblem 1
x + -8.38888889 = 8.481097356 Simplifying x + -8.38888889 = 8.481097356 Reorder the terms: -8.38888889 + x = 8.481097356 Solving -8.38888889 + x = 8.481097356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.38888889' to each side of the equation. -8.38888889 + 8.38888889 + x = 8.481097356 + 8.38888889 Combine like terms: -8.38888889 + 8.38888889 = 0.00000000 0.00000000 + x = 8.481097356 + 8.38888889 x = 8.481097356 + 8.38888889 Combine like terms: 8.481097356 + 8.38888889 = 16.869986246 x = 16.869986246 Simplifying x = 16.869986246Subproblem 2
x + -8.38888889 = -8.481097356 Simplifying x + -8.38888889 = -8.481097356 Reorder the terms: -8.38888889 + x = -8.481097356 Solving -8.38888889 + x = -8.481097356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.38888889' to each side of the equation. -8.38888889 + 8.38888889 + x = -8.481097356 + 8.38888889 Combine like terms: -8.38888889 + 8.38888889 = 0.00000000 0.00000000 + x = -8.481097356 + 8.38888889 x = -8.481097356 + 8.38888889 Combine like terms: -8.481097356 + 8.38888889 = -0.092208466 x = -0.092208466 Simplifying x = -0.092208466Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.869986246, -0.092208466}
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