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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 = 0.0401234568 0.1512345679 + -0.7777777778x + x2 = 0.0401234568 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 0.0401234568 Calculate the square root of the right side: 0.200308404 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 0.200308404 and -0.200308404.Subproblem 1
x + -0.3888888889 = 0.200308404 Simplifying x + -0.3888888889 = 0.200308404 Reorder the terms: -0.3888888889 + x = 0.200308404 Solving -0.3888888889 + x = 0.200308404 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 = 0.200308404 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 0.200308404 + 0.3888888889 x = 0.200308404 + 0.3888888889 Combine like terms: 0.200308404 + 0.3888888889 = 0.5891972929 x = 0.5891972929 Simplifying x = 0.5891972929Subproblem 2
x + -0.3888888889 = -0.200308404 Simplifying x + -0.3888888889 = -0.200308404 Reorder the terms: -0.3888888889 + x = -0.200308404 Solving -0.3888888889 + x = -0.200308404 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 = -0.200308404 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -0.200308404 + 0.3888888889 x = -0.200308404 + 0.3888888889 Combine like terms: -0.200308404 + 0.3888888889 = 0.1885804849 x = 0.1885804849 Simplifying x = 0.1885804849Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5891972929, 0.1885804849}
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