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Simplifying 9x2 = 9 + -2x Solving 9x2 = 9 + -2x Solving for variable 'x'. Reorder the terms: -9 + 2x + 9x2 = 9 + -2x + -9 + 2x Reorder the terms: -9 + 2x + 9x2 = 9 + -9 + -2x + 2x Combine like terms: 9 + -9 = 0 -9 + 2x + 9x2 = 0 + -2x + 2x -9 + 2x + 9x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -9 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.2222222222x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.2222222222x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.2222222222x + x2 = 0 + 1 0.2222222222x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.2222222222x + x2 = 1 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 1 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 1 + 0.01234567901 Combine like terms: 1 + 0.01234567901 = 1.01234567901 0.01234567901 + 0.2222222222x + x2 = 1.01234567901 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 1.01234567901 Calculate the square root of the right side: 1.006153904 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 1.006153904 and -1.006153904.Subproblem 1
x + 0.1111111111 = 1.006153904 Simplifying x + 0.1111111111 = 1.006153904 Reorder the terms: 0.1111111111 + x = 1.006153904 Solving 0.1111111111 + x = 1.006153904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 1.006153904 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.006153904 + -0.1111111111 x = 1.006153904 + -0.1111111111 Combine like terms: 1.006153904 + -0.1111111111 = 0.8950427929 x = 0.8950427929 Simplifying x = 0.8950427929Subproblem 2
x + 0.1111111111 = -1.006153904 Simplifying x + 0.1111111111 = -1.006153904 Reorder the terms: 0.1111111111 + x = -1.006153904 Solving 0.1111111111 + x = -1.006153904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -1.006153904 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.006153904 + -0.1111111111 x = -1.006153904 + -0.1111111111 Combine like terms: -1.006153904 + -0.1111111111 = -1.1172650151 x = -1.1172650151 Simplifying x = -1.1172650151Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8950427929, -1.1172650151}
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