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Simplifying 9x2 + 9x + -2 = 0 Reorder the terms: -2 + 9x + 9x2 = 0 Solving -2 + 9x + 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 + x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.2222222222 x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 x + x2 = 0.2222222222 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.2222222222 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.2222222222 + 0.25 Combine like terms: 0.2222222222 + 0.25 = 0.4722222222 1.25 + x2 = 0.4722222222 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4722222222 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (x + 0.5) equal to 0.687184271 and -0.687184271.Subproblem 1
x + 0.5 = 0.687184271 Simplifying x + 0.5 = 0.687184271 Reorder the terms: 0.5 + x = 0.687184271 Solving 0.5 + x = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.687184271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.687184271 + -0.5 x = 0.687184271 + -0.5 Combine like terms: 0.687184271 + -0.5 = 0.187184271 x = 0.187184271 Simplifying x = 0.187184271Subproblem 2
x + 0.5 = -0.687184271 Simplifying x + 0.5 = -0.687184271 Reorder the terms: 0.5 + x = -0.687184271 Solving 0.5 + x = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.687184271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.687184271 + -0.5 x = -0.687184271 + -0.5 Combine like terms: -0.687184271 + -0.5 = -1.187184271 x = -1.187184271 Simplifying x = -1.187184271Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.187184271, -1.187184271}
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