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Simplifying 9x2 + -20x + 2 = 0 Reorder the terms: 2 + -20x + 9x2 = 0 Solving 2 + -20x + 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 + -2.222222222x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -2.222222222x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -2.222222222x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -2.222222222x + x2 = 0 + -0.2222222222 -2.222222222x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -2.222222222x + x2 = -0.2222222222 The x term is -2.222222222x. Take half its coefficient (-1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. -2.222222222x + 1.234567901 + x2 = -0.2222222222 + 1.234567901 Reorder the terms: 1.234567901 + -2.222222222x + x2 = -0.2222222222 + 1.234567901 Combine like terms: -0.2222222222 + 1.234567901 = 1.0123456788 1.234567901 + -2.222222222x + x2 = 1.0123456788 Factor a perfect square on the left side: (x + -1.111111111)(x + -1.111111111) = 1.0123456788 Calculate the square root of the right side: 1.006153904 Break this problem into two subproblems by setting (x + -1.111111111) equal to 1.006153904 and -1.006153904.Subproblem 1
x + -1.111111111 = 1.006153904 Simplifying x + -1.111111111 = 1.006153904 Reorder the terms: -1.111111111 + x = 1.006153904 Solving -1.111111111 + x = 1.006153904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = 1.006153904 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 1.006153904 + 1.111111111 x = 1.006153904 + 1.111111111 Combine like terms: 1.006153904 + 1.111111111 = 2.117265015 x = 2.117265015 Simplifying x = 2.117265015Subproblem 2
x + -1.111111111 = -1.006153904 Simplifying x + -1.111111111 = -1.006153904 Reorder the terms: -1.111111111 + x = -1.006153904 Solving -1.111111111 + x = -1.006153904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = -1.006153904 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = -1.006153904 + 1.111111111 x = -1.006153904 + 1.111111111 Combine like terms: -1.006153904 + 1.111111111 = 0.104957207 x = 0.104957207 Simplifying x = 0.104957207Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.117265015, 0.104957207}
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