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Simplifying 9x2 + 34x + 16 = 0 Reorder the terms: 16 + 34x + 9x2 = 0 Solving 16 + 34x + 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'. 1.777777778 + 3.777777778x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + 3.777777778x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + 3.777777778x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + 3.777777778x + x2 = 0 + -1.777777778 3.777777778x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 3.777777778x + x2 = -1.777777778 The x term is 3.777777778x. Take half its coefficient (1.888888889). Square it (3.567901235) and add it to both sides. Add '3.567901235' to each side of the equation. 3.777777778x + 3.567901235 + x2 = -1.777777778 + 3.567901235 Reorder the terms: 3.567901235 + 3.777777778x + x2 = -1.777777778 + 3.567901235 Combine like terms: -1.777777778 + 3.567901235 = 1.790123457 3.567901235 + 3.777777778x + x2 = 1.790123457 Factor a perfect square on the left side: (x + 1.888888889)(x + 1.888888889) = 1.790123457 Calculate the square root of the right side: 1.337954953 Break this problem into two subproblems by setting (x + 1.888888889) equal to 1.337954953 and -1.337954953.Subproblem 1
x + 1.888888889 = 1.337954953 Simplifying x + 1.888888889 = 1.337954953 Reorder the terms: 1.888888889 + x = 1.337954953 Solving 1.888888889 + x = 1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.888888889' to each side of the equation. 1.888888889 + -1.888888889 + x = 1.337954953 + -1.888888889 Combine like terms: 1.888888889 + -1.888888889 = 0.000000000 0.000000000 + x = 1.337954953 + -1.888888889 x = 1.337954953 + -1.888888889 Combine like terms: 1.337954953 + -1.888888889 = -0.550933936 x = -0.550933936 Simplifying x = -0.550933936Subproblem 2
x + 1.888888889 = -1.337954953 Simplifying x + 1.888888889 = -1.337954953 Reorder the terms: 1.888888889 + x = -1.337954953 Solving 1.888888889 + x = -1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.888888889' to each side of the equation. 1.888888889 + -1.888888889 + x = -1.337954953 + -1.888888889 Combine like terms: 1.888888889 + -1.888888889 = 0.000000000 0.000000000 + x = -1.337954953 + -1.888888889 x = -1.337954953 + -1.888888889 Combine like terms: -1.337954953 + -1.888888889 = -3.226843842 x = -3.226843842 Simplifying x = -3.226843842Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.550933936, -3.226843842}
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