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Simplifying 9x2 + -18x + 2 = 0 Reorder the terms: 2 + -18x + 9x2 = 0 Solving 2 + -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'. 0.2222222222 + -2x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -2x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -2x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.2222222222 -2x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -2x + x2 = -0.2222222222 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 = -0.2222222222 + 1 Reorder the terms: 1 + -2x + x2 = -0.2222222222 + 1 Combine like terms: -0.2222222222 + 1 = 0.7777777778 1 + -2x + x2 = 0.7777777778 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.7777777778 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (x + -1) equal to 0.881917104 and -0.881917104.Subproblem 1
x + -1 = 0.881917104 Simplifying x + -1 = 0.881917104 Reorder the terms: -1 + x = 0.881917104 Solving -1 + x = 0.881917104 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 = 0.881917104 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.881917104 + 1 x = 0.881917104 + 1 Combine like terms: 0.881917104 + 1 = 1.881917104 x = 1.881917104 Simplifying x = 1.881917104Subproblem 2
x + -1 = -0.881917104 Simplifying x + -1 = -0.881917104 Reorder the terms: -1 + x = -0.881917104 Solving -1 + x = -0.881917104 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 = -0.881917104 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.881917104 + 1 x = -0.881917104 + 1 Combine like terms: -0.881917104 + 1 = 0.118082896 x = 0.118082896 Simplifying x = 0.118082896Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.881917104, 0.118082896}
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