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Simplifying 9x(x + -2) = 2x + -1 Reorder the terms: 9x(-2 + x) = 2x + -1 (-2 * 9x + x * 9x) = 2x + -1 (-18x + 9x2) = 2x + -1 Reorder the terms: -18x + 9x2 = -1 + 2x Solving -18x + 9x2 = -1 + 2x Solving for variable 'x'. Reorder the terms: 1 + -18x + -2x + 9x2 = -1 + 2x + 1 + -2x Combine like terms: -18x + -2x = -20x 1 + -20x + 9x2 = -1 + 2x + 1 + -2x Reorder the terms: 1 + -20x + 9x2 = -1 + 1 + 2x + -2x Combine like terms: -1 + 1 = 0 1 + -20x + 9x2 = 0 + 2x + -2x 1 + -20x + 9x2 = 2x + -2x Combine like terms: 2x + -2x = 0 1 + -20x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -2.222222222x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -2.222222222x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -2.222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -2.222222222x + x2 = 0 + -0.1111111111 -2.222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -2.222222222x + x2 = -0.1111111111 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 = -0.1111111111 + 1.234567901 Reorder the terms: 1.234567901 + -2.222222222x + x2 = -0.1111111111 + 1.234567901 Combine like terms: -0.1111111111 + 1.234567901 = 1.1234567899 1.234567901 + -2.222222222x + x2 = 1.1234567899 Factor a perfect square on the left side: (x + -1.111111111)(x + -1.111111111) = 1.1234567899 Calculate the square root of the right side: 1.059932446 Break this problem into two subproblems by setting (x + -1.111111111) equal to 1.059932446 and -1.059932446.Subproblem 1
x + -1.111111111 = 1.059932446 Simplifying x + -1.111111111 = 1.059932446 Reorder the terms: -1.111111111 + x = 1.059932446 Solving -1.111111111 + x = 1.059932446 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 = 1.059932446 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 1.059932446 + 1.111111111 x = 1.059932446 + 1.111111111 Combine like terms: 1.059932446 + 1.111111111 = 2.171043557 x = 2.171043557 Simplifying x = 2.171043557Subproblem 2
x + -1.111111111 = -1.059932446 Simplifying x + -1.111111111 = -1.059932446 Reorder the terms: -1.111111111 + x = -1.059932446 Solving -1.111111111 + x = -1.059932446 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 = -1.059932446 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = -1.059932446 + 1.111111111 x = -1.059932446 + 1.111111111 Combine like terms: -1.059932446 + 1.111111111 = 0.051178665 x = 0.051178665 Simplifying x = 0.051178665Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.171043557, 0.051178665}
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