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Simplifying 9x2 = 8 + -2x Solving 9x2 = 8 + -2x Solving for variable 'x'. Reorder the terms: -8 + 2x + 9x2 = 8 + -2x + -8 + 2x Reorder the terms: -8 + 2x + 9x2 = 8 + -8 + -2x + 2x Combine like terms: 8 + -8 = 0 -8 + 2x + 9x2 = 0 + -2x + 2x -8 + 2x + 9x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -8 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.2222222222x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.2222222222x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.2222222222x + x2 = 0 + 0.8888888889 0.2222222222x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.2222222222x + x2 = 0.8888888889 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 = 0.8888888889 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.8888888889 + 0.01234567901 Combine like terms: 0.8888888889 + 0.01234567901 = 0.90123456791 0.01234567901 + 0.2222222222x + x2 = 0.90123456791 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.90123456791 Calculate the square root of the right side: 0.949333749 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.949333749 and -0.949333749.Subproblem 1
x + 0.1111111111 = 0.949333749 Simplifying x + 0.1111111111 = 0.949333749 Reorder the terms: 0.1111111111 + x = 0.949333749 Solving 0.1111111111 + x = 0.949333749 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 = 0.949333749 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.949333749 + -0.1111111111 x = 0.949333749 + -0.1111111111 Combine like terms: 0.949333749 + -0.1111111111 = 0.8382226379 x = 0.8382226379 Simplifying x = 0.8382226379Subproblem 2
x + 0.1111111111 = -0.949333749 Simplifying x + 0.1111111111 = -0.949333749 Reorder the terms: 0.1111111111 + x = -0.949333749 Solving 0.1111111111 + x = -0.949333749 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 = -0.949333749 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.949333749 + -0.1111111111 x = -0.949333749 + -0.1111111111 Combine like terms: -0.949333749 + -0.1111111111 = -1.0604448601 x = -1.0604448601 Simplifying x = -1.0604448601Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8382226379, -1.0604448601}
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