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Simplifying 9x2 + x + 2 = 0 Reorder the terms: 2 + x + 9x2 = 0 Solving 2 + x + 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 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 0.1111111111x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 0.1111111111x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 0.1111111111x + x2 = 0 + -0.2222222222 0.1111111111x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 0.1111111111x + 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. 0.1111111111x + 0.25 + x2 = -0.2222222222 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = -0.2222222222 + 0.25 Combine like terms: -0.2222222222 + 0.25 = 0.0277777778 0.25 + 0.1111111111x + x2 = 0.0277777778 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.0277777778 Calculate the square root of the right side: 0.166666667 Break this problem into two subproblems by setting (x + 0.5) equal to 0.166666667 and -0.166666667.Subproblem 1
x + 0.5 = 0.166666667 Simplifying x + 0.5 = 0.166666667 Reorder the terms: 0.5 + x = 0.166666667 Solving 0.5 + x = 0.166666667 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 = 0.166666667 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.166666667 + -0.5 x = 0.166666667 + -0.5 Combine like terms: 0.166666667 + -0.5 = -0.333333333 x = -0.333333333 Simplifying x = -0.333333333Subproblem 2
x + 0.5 = -0.166666667 Simplifying x + 0.5 = -0.166666667 Reorder the terms: 0.5 + x = -0.166666667 Solving 0.5 + x = -0.166666667 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 = -0.166666667 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.166666667 + -0.5 x = -0.166666667 + -0.5 Combine like terms: -0.166666667 + -0.5 = -0.666666667 x = -0.666666667 Simplifying x = -0.666666667Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.333333333, -0.666666667}
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