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Simplifying 9x2 + -34x + -9 = 0 Reorder the terms: -9 + -34x + 9x2 = 0 Solving -9 + -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 + -3.777777778x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.777777778x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.777777778x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.777777778x + x2 = 0 + 1 -3.777777778x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.777777778x + x2 = 1 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 + 3.567901235 Reorder the terms: 3.567901235 + -3.777777778x + x2 = 1 + 3.567901235 Combine like terms: 1 + 3.567901235 = 4.567901235 3.567901235 + -3.777777778x + x2 = 4.567901235 Factor a perfect square on the left side: (x + -1.888888889)(x + -1.888888889) = 4.567901235 Calculate the square root of the right side: 2.137264896 Break this problem into two subproblems by setting (x + -1.888888889) equal to 2.137264896 and -2.137264896.Subproblem 1
x + -1.888888889 = 2.137264896 Simplifying x + -1.888888889 = 2.137264896 Reorder the terms: -1.888888889 + x = 2.137264896 Solving -1.888888889 + x = 2.137264896 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 = 2.137264896 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = 2.137264896 + 1.888888889 x = 2.137264896 + 1.888888889 Combine like terms: 2.137264896 + 1.888888889 = 4.026153785 x = 4.026153785 Simplifying x = 4.026153785Subproblem 2
x + -1.888888889 = -2.137264896 Simplifying x + -1.888888889 = -2.137264896 Reorder the terms: -1.888888889 + x = -2.137264896 Solving -1.888888889 + x = -2.137264896 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 = -2.137264896 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = -2.137264896 + 1.888888889 x = -2.137264896 + 1.888888889 Combine like terms: -2.137264896 + 1.888888889 = -0.248376007 x = -0.248376007 Simplifying x = -0.248376007Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.026153785, -0.248376007}
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