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Simplifying 9x2 + 16x + -357 = 0 Reorder the terms: -357 + 16x + 9x2 = 0 Solving -357 + 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'. -39.66666667 + 1.777777778x + x2 = 0 Move the constant term to the right: Add '39.66666667' to each side of the equation. -39.66666667 + 1.777777778x + 39.66666667 + x2 = 0 + 39.66666667 Reorder the terms: -39.66666667 + 39.66666667 + 1.777777778x + x2 = 0 + 39.66666667 Combine like terms: -39.66666667 + 39.66666667 = 0.00000000 0.00000000 + 1.777777778x + x2 = 0 + 39.66666667 1.777777778x + x2 = 0 + 39.66666667 Combine like terms: 0 + 39.66666667 = 39.66666667 1.777777778x + x2 = 39.66666667 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 = 39.66666667 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778x + x2 = 39.66666667 + 0.7901234570 Combine like terms: 39.66666667 + 0.7901234570 = 40.456790127 0.7901234570 + 1.777777778x + x2 = 40.456790127 Factor a perfect square on the left side: (x + 0.888888889)(x + 0.888888889) = 40.456790127 Calculate the square root of the right side: 6.360565236 Break this problem into two subproblems by setting (x + 0.888888889) equal to 6.360565236 and -6.360565236.Subproblem 1
x + 0.888888889 = 6.360565236 Simplifying x + 0.888888889 = 6.360565236 Reorder the terms: 0.888888889 + x = 6.360565236 Solving 0.888888889 + x = 6.360565236 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 = 6.360565236 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = 6.360565236 + -0.888888889 x = 6.360565236 + -0.888888889 Combine like terms: 6.360565236 + -0.888888889 = 5.471676347 x = 5.471676347 Simplifying x = 5.471676347Subproblem 2
x + 0.888888889 = -6.360565236 Simplifying x + 0.888888889 = -6.360565236 Reorder the terms: 0.888888889 + x = -6.360565236 Solving 0.888888889 + x = -6.360565236 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 = -6.360565236 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = -6.360565236 + -0.888888889 x = -6.360565236 + -0.888888889 Combine like terms: -6.360565236 + -0.888888889 = -7.249454125 x = -7.249454125 Simplifying x = -7.249454125Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.471676347, -7.249454125}
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