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Simplifying 0 = 9x2 + -48x + 44 Reorder the terms: 0 = 44 + -48x + 9x2 Solving 0 = 44 + -48x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -44 = -44 -44 + 48x + -9x2 = 44 + -48x + 9x2 + -44 + 48x + -9x2 Reorder the terms: -44 + 48x + -9x2 = 44 + -44 + -48x + 48x + 9x2 + -9x2 Combine like terms: 44 + -44 = 0 -44 + 48x + -9x2 = 0 + -48x + 48x + 9x2 + -9x2 -44 + 48x + -9x2 = -48x + 48x + 9x2 + -9x2 Combine like terms: -48x + 48x = 0 -44 + 48x + -9x2 = 0 + 9x2 + -9x2 -44 + 48x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -44 + 48x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 4.888888889 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-4.888888889' to each side of the equation. 4.888888889 + -5.333333333x + -4.888888889 + x2 = 0 + -4.888888889 Reorder the terms: 4.888888889 + -4.888888889 + -5.333333333x + x2 = 0 + -4.888888889 Combine like terms: 4.888888889 + -4.888888889 = 0.000000000 0.000000000 + -5.333333333x + x2 = 0 + -4.888888889 -5.333333333x + x2 = 0 + -4.888888889 Combine like terms: 0 + -4.888888889 = -4.888888889 -5.333333333x + x2 = -4.888888889 The x term is -5.333333333x. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333x + 7.111111113 + x2 = -4.888888889 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -4.888888889 + 7.111111113 Combine like terms: -4.888888889 + 7.111111113 = 2.222222224 7.111111113 + -5.333333333x + x2 = 2.222222224 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 2.222222224 Calculate the square root of the right side: 1.490711986 Break this problem into two subproblems by setting (x + -2.666666667) equal to 1.490711986 and -1.490711986.Subproblem 1
x + -2.666666667 = 1.490711986 Simplifying x + -2.666666667 = 1.490711986 Reorder the terms: -2.666666667 + x = 1.490711986 Solving -2.666666667 + x = 1.490711986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = 1.490711986 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 1.490711986 + 2.666666667 x = 1.490711986 + 2.666666667 Combine like terms: 1.490711986 + 2.666666667 = 4.157378653 x = 4.157378653 Simplifying x = 4.157378653Subproblem 2
x + -2.666666667 = -1.490711986 Simplifying x + -2.666666667 = -1.490711986 Reorder the terms: -2.666666667 + x = -1.490711986 Solving -2.666666667 + x = -1.490711986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = -1.490711986 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -1.490711986 + 2.666666667 x = -1.490711986 + 2.666666667 Combine like terms: -1.490711986 + 2.666666667 = 1.175954681 x = 1.175954681 Simplifying x = 1.175954681Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.157378653, 1.175954681}
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