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Simplifying 0 = (-9x2) + 16x + 48 Reorder the terms: 0 = 48 + 16x + (-9x2) Solving 0 = 48 + 16x + (-9x2) Solving for variable 'x'. Combine like terms: 0 + -48 = -48 -48 + -16x + (9x2) = 48 + 16x + (-9x2) + -48 + -16x + (9x2) Reorder the terms: -48 + -16x + (9x2) = 48 + -48 + 16x + -16x + (-9x2) + (9x2) Combine like terms: 48 + -48 = 0 -48 + -16x + (9x2) = 0 + 16x + -16x + (-9x2) + (9x2) -48 + -16x + (9x2) = 16x + -16x + (-9x2) + (9x2) Combine like terms: 16x + -16x = 0 -48 + -16x + (9x2) = 0 + (-9x2) + (9x2) -48 + -16x + (9x2) = (-9x2) + (9x2) Combine like terms: (-9x2) + (9x2) = 0 -48 + -16x + (9x2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.333333333 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -1.777777778x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -1.777777778x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -1.777777778x + x2 = 0 + 5.333333333 -1.777777778x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -1.777777778x + x2 = 5.333333333 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 = 5.333333333 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 5.333333333 + 0.7901234570 Combine like terms: 5.333333333 + 0.7901234570 = 6.12345679 0.7901234570 + -1.777777778x + x2 = 6.12345679 Factor a perfect square on the left side: ((x) + -0.888888889)((x) + -0.888888889) = 6.12345679 Calculate the square root of the right side: 2.474561939 Break this problem into two subproblems by setting ((x) + -0.888888889) equal to 2.474561939 and -2.474561939.Subproblem 1
(x) + -0.888888889 = 2.474561939 Simplifying (x) + -0.888888889 = 2.474561939 x + -0.888888889 = 2.474561939 Reorder the terms: -0.888888889 + x = 2.474561939 Solving -0.888888889 + x = 2.474561939 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 = 2.474561939 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 2.474561939 + 0.888888889 x = 2.474561939 + 0.888888889 Combine like terms: 2.474561939 + 0.888888889 = 3.363450828 x = 3.363450828 Simplifying x = 3.363450828Subproblem 2
(x) + -0.888888889 = -2.474561939 Simplifying (x) + -0.888888889 = -2.474561939 x + -0.888888889 = -2.474561939 Reorder the terms: -0.888888889 + x = -2.474561939 Solving -0.888888889 + x = -2.474561939 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 = -2.474561939 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -2.474561939 + 0.888888889 x = -2.474561939 + 0.888888889 Combine like terms: -2.474561939 + 0.888888889 = -1.58567305 x = -1.58567305 Simplifying x = -1.58567305Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.363450828, -1.58567305}
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