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Simplifying -9x2 + 2x + 8 = 0 Reorder the terms: 8 + 2x + -9x2 = 0 Solving 8 + 2x + -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'. -0.8888888889 + -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 = 1.0604448601 x = 1.0604448601 Simplifying x = 1.0604448601Subproblem 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 = -0.8382226379 x = -0.8382226379 Simplifying x = -0.8382226379Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0604448601, -0.8382226379}
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