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Simplifying 0 = 9x2 + -16x + -44 Reorder the terms: 0 = -44 + -16x + 9x2 Solving 0 = -44 + -16x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 44 = 44 44 + 16x + -9x2 = -44 + -16x + 9x2 + 44 + 16x + -9x2 Reorder the terms: 44 + 16x + -9x2 = -44 + 44 + -16x + 16x + 9x2 + -9x2 Combine like terms: -44 + 44 = 0 44 + 16x + -9x2 = 0 + -16x + 16x + 9x2 + -9x2 44 + 16x + -9x2 = -16x + 16x + 9x2 + -9x2 Combine like terms: -16x + 16x = 0 44 + 16x + -9x2 = 0 + 9x2 + -9x2 44 + 16x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 44 + 16x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -4.888888889 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '4.888888889' to each side of the equation. -4.888888889 + -1.777777778x + 4.888888889 + x2 = 0 + 4.888888889 Reorder the terms: -4.888888889 + 4.888888889 + -1.777777778x + x2 = 0 + 4.888888889 Combine like terms: -4.888888889 + 4.888888889 = 0.000000000 0.000000000 + -1.777777778x + x2 = 0 + 4.888888889 -1.777777778x + x2 = 0 + 4.888888889 Combine like terms: 0 + 4.888888889 = 4.888888889 -1.777777778x + x2 = 4.888888889 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 = 4.888888889 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 4.888888889 + 0.7901234570 Combine like terms: 4.888888889 + 0.7901234570 = 5.679012346 0.7901234570 + -1.777777778x + x2 = 5.679012346 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 5.679012346 Calculate the square root of the right side: 2.383067843 Break this problem into two subproblems by setting (x + -0.888888889) equal to 2.383067843 and -2.383067843.Subproblem 1
x + -0.888888889 = 2.383067843 Simplifying x + -0.888888889 = 2.383067843 Reorder the terms: -0.888888889 + x = 2.383067843 Solving -0.888888889 + x = 2.383067843 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 = 2.383067843 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 2.383067843 + 0.888888889 x = 2.383067843 + 0.888888889 Combine like terms: 2.383067843 + 0.888888889 = 3.271956732 x = 3.271956732 Simplifying x = 3.271956732Subproblem 2
x + -0.888888889 = -2.383067843 Simplifying x + -0.888888889 = -2.383067843 Reorder the terms: -0.888888889 + x = -2.383067843 Solving -0.888888889 + x = -2.383067843 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 = -2.383067843 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -2.383067843 + 0.888888889 x = -2.383067843 + 0.888888889 Combine like terms: -2.383067843 + 0.888888889 = -1.494178954 x = -1.494178954 Simplifying x = -1.494178954Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.271956732, -1.494178954}
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