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Simplifying 9x2 + -214x + 1089 = 0 Reorder the terms: 1089 + -214x + 9x2 = 0 Solving 1089 + -214x + 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'. 121 + -23.77777778x + x2 = 0 Move the constant term to the right: Add '-121' to each side of the equation. 121 + -23.77777778x + -121 + x2 = 0 + -121 Reorder the terms: 121 + -121 + -23.77777778x + x2 = 0 + -121 Combine like terms: 121 + -121 = 0 0 + -23.77777778x + x2 = 0 + -121 -23.77777778x + x2 = 0 + -121 Combine like terms: 0 + -121 = -121 -23.77777778x + x2 = -121 The x term is -23.77777778x. Take half its coefficient (-11.88888889). Square it (141.3456790) and add it to both sides. Add '141.3456790' to each side of the equation. -23.77777778x + 141.3456790 + x2 = -121 + 141.3456790 Reorder the terms: 141.3456790 + -23.77777778x + x2 = -121 + 141.3456790 Combine like terms: -121 + 141.3456790 = 20.345679 141.3456790 + -23.77777778x + x2 = 20.345679 Factor a perfect square on the left side: (x + -11.88888889)(x + -11.88888889) = 20.345679 Calculate the square root of the right side: 4.510618472 Break this problem into two subproblems by setting (x + -11.88888889) equal to 4.510618472 and -4.510618472.Subproblem 1
x + -11.88888889 = 4.510618472 Simplifying x + -11.88888889 = 4.510618472 Reorder the terms: -11.88888889 + x = 4.510618472 Solving -11.88888889 + x = 4.510618472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.88888889' to each side of the equation. -11.88888889 + 11.88888889 + x = 4.510618472 + 11.88888889 Combine like terms: -11.88888889 + 11.88888889 = 0.00000000 0.00000000 + x = 4.510618472 + 11.88888889 x = 4.510618472 + 11.88888889 Combine like terms: 4.510618472 + 11.88888889 = 16.399507362 x = 16.399507362 Simplifying x = 16.399507362Subproblem 2
x + -11.88888889 = -4.510618472 Simplifying x + -11.88888889 = -4.510618472 Reorder the terms: -11.88888889 + x = -4.510618472 Solving -11.88888889 + x = -4.510618472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.88888889' to each side of the equation. -11.88888889 + 11.88888889 + x = -4.510618472 + 11.88888889 Combine like terms: -11.88888889 + 11.88888889 = 0.00000000 0.00000000 + x = -4.510618472 + 11.88888889 x = -4.510618472 + 11.88888889 Combine like terms: -4.510618472 + 11.88888889 = 7.378270418 x = 7.378270418 Simplifying x = 7.378270418Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.399507362, 7.378270418}
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