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Simplifying 0 = 9x2 + -52x + 4 Reorder the terms: 0 = 4 + -52x + 9x2 Solving 0 = 4 + -52x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 52x + -9x2 = 4 + -52x + 9x2 + -4 + 52x + -9x2 Reorder the terms: -4 + 52x + -9x2 = 4 + -4 + -52x + 52x + 9x2 + -9x2 Combine like terms: 4 + -4 = 0 -4 + 52x + -9x2 = 0 + -52x + 52x + 9x2 + -9x2 -4 + 52x + -9x2 = -52x + 52x + 9x2 + -9x2 Combine like terms: -52x + 52x = 0 -4 + 52x + -9x2 = 0 + 9x2 + -9x2 -4 + 52x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -4 + 52x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.4444444444 + -5.777777778x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -5.777777778x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -5.777777778x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -5.777777778x + x2 = 0 + -0.4444444444 -5.777777778x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -5.777777778x + x2 = -0.4444444444 The x term is -5.777777778x. Take half its coefficient (-2.888888889). Square it (8.345679013) and add it to both sides. Add '8.345679013' to each side of the equation. -5.777777778x + 8.345679013 + x2 = -0.4444444444 + 8.345679013 Reorder the terms: 8.345679013 + -5.777777778x + x2 = -0.4444444444 + 8.345679013 Combine like terms: -0.4444444444 + 8.345679013 = 7.9012345686 8.345679013 + -5.777777778x + x2 = 7.9012345686 Factor a perfect square on the left side: (x + -2.888888889)(x + -2.888888889) = 7.9012345686 Calculate the square root of the right side: 2.810913476 Break this problem into two subproblems by setting (x + -2.888888889) equal to 2.810913476 and -2.810913476.Subproblem 1
x + -2.888888889 = 2.810913476 Simplifying x + -2.888888889 = 2.810913476 Reorder the terms: -2.888888889 + x = 2.810913476 Solving -2.888888889 + x = 2.810913476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.888888889' to each side of the equation. -2.888888889 + 2.888888889 + x = 2.810913476 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + x = 2.810913476 + 2.888888889 x = 2.810913476 + 2.888888889 Combine like terms: 2.810913476 + 2.888888889 = 5.699802365 x = 5.699802365 Simplifying x = 5.699802365Subproblem 2
x + -2.888888889 = -2.810913476 Simplifying x + -2.888888889 = -2.810913476 Reorder the terms: -2.888888889 + x = -2.810913476 Solving -2.888888889 + x = -2.810913476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.888888889' to each side of the equation. -2.888888889 + 2.888888889 + x = -2.810913476 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + x = -2.810913476 + 2.888888889 x = -2.810913476 + 2.888888889 Combine like terms: -2.810913476 + 2.888888889 = 0.077975413 x = 0.077975413 Simplifying x = 0.077975413Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.699802365, 0.077975413}
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