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Simplifying 2x2 + 11x + -1 = 0 Reorder the terms: -1 + 11x + 2x2 = 0 Solving -1 + 11x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 5.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 5.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 5.5x + x2 = 0 + 0.5 5.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 5.5x + x2 = 0.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 0.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 0.5 + 7.5625 Combine like terms: 0.5 + 7.5625 = 8.0625 7.5625 + 5.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + 2.75) equal to 2.839454173 and -2.839454173.Subproblem 1
x + 2.75 = 2.839454173 Simplifying x + 2.75 = 2.839454173 Reorder the terms: 2.75 + x = 2.839454173 Solving 2.75 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.839454173 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.839454173 + -2.75 x = 2.839454173 + -2.75 Combine like terms: 2.839454173 + -2.75 = 0.089454173 x = 0.089454173 Simplifying x = 0.089454173Subproblem 2
x + 2.75 = -2.839454173 Simplifying x + 2.75 = -2.839454173 Reorder the terms: 2.75 + x = -2.839454173 Solving 2.75 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.839454173 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.839454173 + -2.75 x = -2.839454173 + -2.75 Combine like terms: -2.839454173 + -2.75 = -5.589454173 x = -5.589454173 Simplifying x = -5.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.089454173, -5.589454173}
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