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Simplifying 9x2 + -1096x + 13456 = 0 Reorder the terms: 13456 + -1096x + 9x2 = 0 Solving 13456 + -1096x + 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'. 1495.111111 + -121.7777778x + x2 = 0 Move the constant term to the right: Add '-1495.111111' to each side of the equation. 1495.111111 + -121.7777778x + -1495.111111 + x2 = 0 + -1495.111111 Reorder the terms: 1495.111111 + -1495.111111 + -121.7777778x + x2 = 0 + -1495.111111 Combine like terms: 1495.111111 + -1495.111111 = 0.000000 0.000000 + -121.7777778x + x2 = 0 + -1495.111111 -121.7777778x + x2 = 0 + -1495.111111 Combine like terms: 0 + -1495.111111 = -1495.111111 -121.7777778x + x2 = -1495.111111 The x term is -121.7777778x. Take half its coefficient (-60.8888889). Square it (3707.456791) and add it to both sides. Add '3707.456791' to each side of the equation. -121.7777778x + 3707.456791 + x2 = -1495.111111 + 3707.456791 Reorder the terms: 3707.456791 + -121.7777778x + x2 = -1495.111111 + 3707.456791 Combine like terms: -1495.111111 + 3707.456791 = 2212.34568 3707.456791 + -121.7777778x + x2 = 2212.34568 Factor a perfect square on the left side: (x + -60.8888889)(x + -60.8888889) = 2212.34568 Calculate the square root of the right side: 47.035578874 Break this problem into two subproblems by setting (x + -60.8888889) equal to 47.035578874 and -47.035578874.Subproblem 1
x + -60.8888889 = 47.035578874 Simplifying x + -60.8888889 = 47.035578874 Reorder the terms: -60.8888889 + x = 47.035578874 Solving -60.8888889 + x = 47.035578874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.8888889' to each side of the equation. -60.8888889 + 60.8888889 + x = 47.035578874 + 60.8888889 Combine like terms: -60.8888889 + 60.8888889 = 0.0000000 0.0000000 + x = 47.035578874 + 60.8888889 x = 47.035578874 + 60.8888889 Combine like terms: 47.035578874 + 60.8888889 = 107.924467774 x = 107.924467774 Simplifying x = 107.924467774Subproblem 2
x + -60.8888889 = -47.035578874 Simplifying x + -60.8888889 = -47.035578874 Reorder the terms: -60.8888889 + x = -47.035578874 Solving -60.8888889 + x = -47.035578874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.8888889' to each side of the equation. -60.8888889 + 60.8888889 + x = -47.035578874 + 60.8888889 Combine like terms: -60.8888889 + 60.8888889 = 0.0000000 0.0000000 + x = -47.035578874 + 60.8888889 x = -47.035578874 + 60.8888889 Combine like terms: -47.035578874 + 60.8888889 = 13.853310026 x = 13.853310026 Simplifying x = 13.853310026Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.924467774, 13.853310026}
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