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Simplifying -9x2 + 7x + 1 = 0 Reorder the terms: 1 + 7x + -9x2 = 0 Solving 1 + 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'. -0.1111111111 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.7777777778x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.7777777778x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.7777777778x + x2 = 0 + 0.1111111111 -0.7777777778x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.7777777778x + x2 = 0.1111111111 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 = 0.1111111111 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 0.1111111111 + 0.1512345679 Combine like terms: 0.1111111111 + 0.1512345679 = 0.262345679 0.1512345679 + -0.7777777778x + x2 = 0.262345679 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 0.262345679 Calculate the square root of the right side: 0.512196914 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 0.512196914 and -0.512196914.Subproblem 1
x + -0.3888888889 = 0.512196914 Simplifying x + -0.3888888889 = 0.512196914 Reorder the terms: -0.3888888889 + x = 0.512196914 Solving -0.3888888889 + x = 0.512196914 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 = 0.512196914 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 0.512196914 + 0.3888888889 x = 0.512196914 + 0.3888888889 Combine like terms: 0.512196914 + 0.3888888889 = 0.9010858029 x = 0.9010858029 Simplifying x = 0.9010858029Subproblem 2
x + -0.3888888889 = -0.512196914 Simplifying x + -0.3888888889 = -0.512196914 Reorder the terms: -0.3888888889 + x = -0.512196914 Solving -0.3888888889 + x = -0.512196914 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 = -0.512196914 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -0.512196914 + 0.3888888889 x = -0.512196914 + 0.3888888889 Combine like terms: -0.512196914 + 0.3888888889 = -0.1233080251 x = -0.1233080251 Simplifying x = -0.1233080251Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9010858029, -0.1233080251}
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