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Simplifying -9x2 + 16x + -2 = 0 Reorder the terms: -2 + 16x + -9x2 = 0 Solving -2 + 16x + -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'. 0.2222222222 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -1.777777778x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -1.777777778x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -1.777777778x + x2 = 0 + -0.2222222222 -1.777777778x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -1.777777778x + x2 = -0.2222222222 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 = -0.2222222222 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = -0.2222222222 + 0.7901234570 Combine like terms: -0.2222222222 + 0.7901234570 = 0.5679012348 0.7901234570 + -1.777777778x + x2 = 0.5679012348 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 0.5679012348 Calculate the square root of the right side: 0.753592221 Break this problem into two subproblems by setting (x + -0.888888889) equal to 0.753592221 and -0.753592221.Subproblem 1
x + -0.888888889 = 0.753592221 Simplifying x + -0.888888889 = 0.753592221 Reorder the terms: -0.888888889 + x = 0.753592221 Solving -0.888888889 + x = 0.753592221 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 = 0.753592221 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 0.753592221 + 0.888888889 x = 0.753592221 + 0.888888889 Combine like terms: 0.753592221 + 0.888888889 = 1.64248111 x = 1.64248111 Simplifying x = 1.64248111Subproblem 2
x + -0.888888889 = -0.753592221 Simplifying x + -0.888888889 = -0.753592221 Reorder the terms: -0.888888889 + x = -0.753592221 Solving -0.888888889 + x = -0.753592221 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 = -0.753592221 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -0.753592221 + 0.888888889 x = -0.753592221 + 0.888888889 Combine like terms: -0.753592221 + 0.888888889 = 0.135296668 x = 0.135296668 Simplifying x = 0.135296668Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.64248111, 0.135296668}
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