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Simplifying 9x2 + -18x + -1 = 0 Reorder the terms: -1 + -18x + 9x2 = 0 Solving -1 + -18x + 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 + -2x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -2x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -2x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.1111111111 -2x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -2x + x2 = 0.1111111111 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.1111111111 + 1 Reorder the terms: 1 + -2x + x2 = 0.1111111111 + 1 Combine like terms: 0.1111111111 + 1 = 1.1111111111 1 + -2x + x2 = 1.1111111111 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.1111111111 Calculate the square root of the right side: 1.054092553 Break this problem into two subproblems by setting (x + -1) equal to 1.054092553 and -1.054092553.Subproblem 1
x + -1 = 1.054092553 Simplifying x + -1 = 1.054092553 Reorder the terms: -1 + x = 1.054092553 Solving -1 + x = 1.054092553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.054092553 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.054092553 + 1 x = 1.054092553 + 1 Combine like terms: 1.054092553 + 1 = 2.054092553 x = 2.054092553 Simplifying x = 2.054092553Subproblem 2
x + -1 = -1.054092553 Simplifying x + -1 = -1.054092553 Reorder the terms: -1 + x = -1.054092553 Solving -1 + x = -1.054092553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.054092553 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.054092553 + 1 x = -1.054092553 + 1 Combine like terms: -1.054092553 + 1 = -0.054092553 x = -0.054092553 Simplifying x = -0.054092553Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.054092553, -0.054092553}
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