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Simplifying 9x2 + -151x + -4878 = 0 Reorder the terms: -4878 + -151x + 9x2 = 0 Solving -4878 + -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'. -542 + -16.77777778x + x2 = 0 Move the constant term to the right: Add '542' to each side of the equation. -542 + -16.77777778x + 542 + x2 = 0 + 542 Reorder the terms: -542 + 542 + -16.77777778x + x2 = 0 + 542 Combine like terms: -542 + 542 = 0 0 + -16.77777778x + x2 = 0 + 542 -16.77777778x + x2 = 0 + 542 Combine like terms: 0 + 542 = 542 -16.77777778x + x2 = 542 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 = 542 + 70.37345681 Reorder the terms: 70.37345681 + -16.77777778x + x2 = 542 + 70.37345681 Combine like terms: 542 + 70.37345681 = 612.37345681 70.37345681 + -16.77777778x + x2 = 612.37345681 Factor a perfect square on the left side: (x + -8.38888889)(x + -8.38888889) = 612.37345681 Calculate the square root of the right side: 24.746180651 Break this problem into two subproblems by setting (x + -8.38888889) equal to 24.746180651 and -24.746180651.Subproblem 1
x + -8.38888889 = 24.746180651 Simplifying x + -8.38888889 = 24.746180651 Reorder the terms: -8.38888889 + x = 24.746180651 Solving -8.38888889 + x = 24.746180651 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 = 24.746180651 + 8.38888889 Combine like terms: -8.38888889 + 8.38888889 = 0.00000000 0.00000000 + x = 24.746180651 + 8.38888889 x = 24.746180651 + 8.38888889 Combine like terms: 24.746180651 + 8.38888889 = 33.135069541 x = 33.135069541 Simplifying x = 33.135069541Subproblem 2
x + -8.38888889 = -24.746180651 Simplifying x + -8.38888889 = -24.746180651 Reorder the terms: -8.38888889 + x = -24.746180651 Solving -8.38888889 + x = -24.746180651 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 = -24.746180651 + 8.38888889 Combine like terms: -8.38888889 + 8.38888889 = 0.00000000 0.00000000 + x = -24.746180651 + 8.38888889 x = -24.746180651 + 8.38888889 Combine like terms: -24.746180651 + 8.38888889 = -16.357291761 x = -16.357291761 Simplifying x = -16.357291761Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.135069541, -16.357291761}
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