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Simplifying x2 + 11x + -27 = 0 Reorder the terms: -27 + 11x + x2 = 0 Solving -27 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 11x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 11x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 11x + x2 = 0 + 27 11x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 11x + x2 = 27 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 27 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 27 + 30.25 Combine like terms: 27 + 30.25 = 57.25 30.25 + 11x + x2 = 57.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + 5.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + 5.5 = 7.566372975 Simplifying x + 5.5 = 7.566372975 Reorder the terms: 5.5 + x = 7.566372975 Solving 5.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.566372975 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.566372975 + -5.5 x = 7.566372975 + -5.5 Combine like terms: 7.566372975 + -5.5 = 2.066372975 x = 2.066372975 Simplifying x = 2.066372975Subproblem 2
x + 5.5 = -7.566372975 Simplifying x + 5.5 = -7.566372975 Reorder the terms: 5.5 + x = -7.566372975 Solving 5.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.566372975 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.566372975 + -5.5 x = -7.566372975 + -5.5 Combine like terms: -7.566372975 + -5.5 = -13.066372975 x = -13.066372975 Simplifying x = -13.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.066372975, -13.066372975}
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