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Simplifying 9x2 + 23x + -11 = 0 Reorder the terms: -11 + 23x + 9x2 = 0 Solving -11 + 23x + 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'. -1.222222222 + 2.555555556x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 2.555555556x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 2.555555556x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 2.555555556x + x2 = 0 + 1.222222222 2.555555556x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 2.555555556x + x2 = 1.222222222 The x term is 2.555555556x. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556x + 1.632716050 + x2 = 1.222222222 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556x + x2 = 1.222222222 + 1.632716050 Combine like terms: 1.222222222 + 1.632716050 = 2.854938272 1.632716050 + 2.555555556x + x2 = 2.854938272 Factor a perfect square on the left side: (x + 1.277777778)(x + 1.277777778) = 2.854938272 Calculate the square root of the right side: 1.689656259 Break this problem into two subproblems by setting (x + 1.277777778) equal to 1.689656259 and -1.689656259.Subproblem 1
x + 1.277777778 = 1.689656259 Simplifying x + 1.277777778 = 1.689656259 Reorder the terms: 1.277777778 + x = 1.689656259 Solving 1.277777778 + x = 1.689656259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = 1.689656259 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = 1.689656259 + -1.277777778 x = 1.689656259 + -1.277777778 Combine like terms: 1.689656259 + -1.277777778 = 0.411878481 x = 0.411878481 Simplifying x = 0.411878481Subproblem 2
x + 1.277777778 = -1.689656259 Simplifying x + 1.277777778 = -1.689656259 Reorder the terms: 1.277777778 + x = -1.689656259 Solving 1.277777778 + x = -1.689656259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + x = -1.689656259 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + x = -1.689656259 + -1.277777778 x = -1.689656259 + -1.277777778 Combine like terms: -1.689656259 + -1.277777778 = -2.967434037 x = -2.967434037 Simplifying x = -2.967434037Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.411878481, -2.967434037}
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