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Simplifying 2x2 + -11x + -11 = 0 Reorder the terms: -11 + -11x + 2x2 = 0 Solving -11 + -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'. -5.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -5.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -5.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -5.5x + x2 = 0 + 5.5 -5.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -5.5x + x2 = 5.5 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 = 5.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 5.5 + 7.5625 Combine like terms: 5.5 + 7.5625 = 13.0625 7.5625 + -5.5x + x2 = 13.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (x + -2.75) equal to 3.614208074 and -3.614208074.Subproblem 1
x + -2.75 = 3.614208074 Simplifying x + -2.75 = 3.614208074 Reorder the terms: -2.75 + x = 3.614208074 Solving -2.75 + x = 3.614208074 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 = 3.614208074 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.614208074 + 2.75 x = 3.614208074 + 2.75 Combine like terms: 3.614208074 + 2.75 = 6.364208074 x = 6.364208074 Simplifying x = 6.364208074Subproblem 2
x + -2.75 = -3.614208074 Simplifying x + -2.75 = -3.614208074 Reorder the terms: -2.75 + x = -3.614208074 Solving -2.75 + x = -3.614208074 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 = -3.614208074 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.614208074 + 2.75 x = -3.614208074 + 2.75 Combine like terms: -3.614208074 + 2.75 = -0.864208074 x = -0.864208074 Simplifying x = -0.864208074Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.364208074, -0.864208074}
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