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Simplifying 9x2 + -16x + -64 = 0 Reorder the terms: -64 + -16x + 9x2 = 0 Solving -64 + -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'. -7.111111111 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '7.111111111' to each side of the equation. -7.111111111 + -1.777777778x + 7.111111111 + x2 = 0 + 7.111111111 Reorder the terms: -7.111111111 + 7.111111111 + -1.777777778x + x2 = 0 + 7.111111111 Combine like terms: -7.111111111 + 7.111111111 = 0.000000000 0.000000000 + -1.777777778x + x2 = 0 + 7.111111111 -1.777777778x + x2 = 0 + 7.111111111 Combine like terms: 0 + 7.111111111 = 7.111111111 -1.777777778x + x2 = 7.111111111 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 = 7.111111111 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 7.111111111 + 0.7901234570 Combine like terms: 7.111111111 + 0.7901234570 = 7.901234568 0.7901234570 + -1.777777778x + x2 = 7.901234568 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 7.901234568 Calculate the square root of the right side: 2.810913476 Break this problem into two subproblems by setting (x + -0.888888889) equal to 2.810913476 and -2.810913476.Subproblem 1
x + -0.888888889 = 2.810913476 Simplifying x + -0.888888889 = 2.810913476 Reorder the terms: -0.888888889 + x = 2.810913476 Solving -0.888888889 + x = 2.810913476 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 = 2.810913476 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 2.810913476 + 0.888888889 x = 2.810913476 + 0.888888889 Combine like terms: 2.810913476 + 0.888888889 = 3.699802365 x = 3.699802365 Simplifying x = 3.699802365Subproblem 2
x + -0.888888889 = -2.810913476 Simplifying x + -0.888888889 = -2.810913476 Reorder the terms: -0.888888889 + x = -2.810913476 Solving -0.888888889 + x = -2.810913476 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 = -2.810913476 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -2.810913476 + 0.888888889 x = -2.810913476 + 0.888888889 Combine like terms: -2.810913476 + 0.888888889 = -1.922024587 x = -1.922024587 Simplifying x = -1.922024587Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.699802365, -1.922024587}
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