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Simplifying 11x2 + -55x + -218 = 0 Reorder the terms: -218 + -55x + 11x2 = 0 Solving -218 + -55x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -19.81818182 + -5x + x2 = 0 Move the constant term to the right: Add '19.81818182' to each side of the equation. -19.81818182 + -5x + 19.81818182 + x2 = 0 + 19.81818182 Reorder the terms: -19.81818182 + 19.81818182 + -5x + x2 = 0 + 19.81818182 Combine like terms: -19.81818182 + 19.81818182 = 0.00000000 0.00000000 + -5x + x2 = 0 + 19.81818182 -5x + x2 = 0 + 19.81818182 Combine like terms: 0 + 19.81818182 = 19.81818182 -5x + x2 = 19.81818182 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 19.81818182 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 19.81818182 + 6.25 Combine like terms: 19.81818182 + 6.25 = 26.06818182 6.25 + -5x + x2 = 26.06818182 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 26.06818182 Calculate the square root of the right side: 5.105700914 Break this problem into two subproblems by setting (x + -2.5) equal to 5.105700914 and -5.105700914.Subproblem 1
x + -2.5 = 5.105700914 Simplifying x + -2.5 = 5.105700914 Reorder the terms: -2.5 + x = 5.105700914 Solving -2.5 + x = 5.105700914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.105700914 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.105700914 + 2.5 x = 5.105700914 + 2.5 Combine like terms: 5.105700914 + 2.5 = 7.605700914 x = 7.605700914 Simplifying x = 7.605700914Subproblem 2
x + -2.5 = -5.105700914 Simplifying x + -2.5 = -5.105700914 Reorder the terms: -2.5 + x = -5.105700914 Solving -2.5 + x = -5.105700914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.105700914 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.105700914 + 2.5 x = -5.105700914 + 2.5 Combine like terms: -5.105700914 + 2.5 = -2.605700914 x = -2.605700914 Simplifying x = -2.605700914Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.605700914, -2.605700914}
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