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Simplifying 9x2 + -7x + -85 = 0 Reorder the terms: -85 + -7x + 9x2 = 0 Solving -85 + -7x + 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'. -9.444444444 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '9.444444444' to each side of the equation. -9.444444444 + -0.7777777778x + 9.444444444 + x2 = 0 + 9.444444444 Reorder the terms: -9.444444444 + 9.444444444 + -0.7777777778x + x2 = 0 + 9.444444444 Combine like terms: -9.444444444 + 9.444444444 = 0.000000000 0.000000000 + -0.7777777778x + x2 = 0 + 9.444444444 -0.7777777778x + x2 = 0 + 9.444444444 Combine like terms: 0 + 9.444444444 = 9.444444444 -0.7777777778x + x2 = 9.444444444 The x term is -0.7777777778x. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778x + 0.1512345679 + x2 = 9.444444444 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 9.444444444 + 0.1512345679 Combine like terms: 9.444444444 + 0.1512345679 = 9.5956790119 0.1512345679 + -0.7777777778x + x2 = 9.5956790119 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 9.5956790119 Calculate the square root of the right side: 3.097689302 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 3.097689302 and -3.097689302.Subproblem 1
x + -0.3888888889 = 3.097689302 Simplifying x + -0.3888888889 = 3.097689302 Reorder the terms: -0.3888888889 + x = 3.097689302 Solving -0.3888888889 + x = 3.097689302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = 3.097689302 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 3.097689302 + 0.3888888889 x = 3.097689302 + 0.3888888889 Combine like terms: 3.097689302 + 0.3888888889 = 3.4865781909 x = 3.4865781909 Simplifying x = 3.4865781909Subproblem 2
x + -0.3888888889 = -3.097689302 Simplifying x + -0.3888888889 = -3.097689302 Reorder the terms: -0.3888888889 + x = -3.097689302 Solving -0.3888888889 + x = -3.097689302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = -3.097689302 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -3.097689302 + 0.3888888889 x = -3.097689302 + 0.3888888889 Combine like terms: -3.097689302 + 0.3888888889 = -2.7088004131 x = -2.7088004131 Simplifying x = -2.7088004131Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4865781909, -2.7088004131}
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