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Simplifying 2x2 + 11x + -22 = 0 Reorder the terms: -22 + 11x + 2x2 = 0 Solving -22 + 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'. -11 + 5.5x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 5.5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 5.5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5.5x + x2 = 0 + 11 5.5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 5.5x + x2 = 11 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 = 11 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 11 + 7.5625 Combine like terms: 11 + 7.5625 = 18.5625 7.5625 + 5.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + 2.75) equal to 4.308421985 and -4.308421985.Subproblem 1
x + 2.75 = 4.308421985 Simplifying x + 2.75 = 4.308421985 Reorder the terms: 2.75 + x = 4.308421985 Solving 2.75 + x = 4.308421985 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 = 4.308421985 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.308421985 + -2.75 x = 4.308421985 + -2.75 Combine like terms: 4.308421985 + -2.75 = 1.558421985 x = 1.558421985 Simplifying x = 1.558421985Subproblem 2
x + 2.75 = -4.308421985 Simplifying x + 2.75 = -4.308421985 Reorder the terms: 2.75 + x = -4.308421985 Solving 2.75 + x = -4.308421985 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 = -4.308421985 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.308421985 + -2.75 x = -4.308421985 + -2.75 Combine like terms: -4.308421985 + -2.75 = -7.058421985 x = -7.058421985 Simplifying x = -7.058421985Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.558421985, -7.058421985}
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