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Simplifying x2 + 27x + -61 = 0 Reorder the terms: -61 + 27x + x2 = 0 Solving -61 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 27x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 27x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 27x + x2 = 0 + 61 27x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 27x + x2 = 61 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 61 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 61 + 182.25 Combine like terms: 61 + 182.25 = 243.25 182.25 + 27x + x2 = 243.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 243.25 Calculate the square root of the right side: 15.59647396 Break this problem into two subproblems by setting (x + 13.5) equal to 15.59647396 and -15.59647396.Subproblem 1
x + 13.5 = 15.59647396 Simplifying x + 13.5 = 15.59647396 Reorder the terms: 13.5 + x = 15.59647396 Solving 13.5 + x = 15.59647396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 15.59647396 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 15.59647396 + -13.5 x = 15.59647396 + -13.5 Combine like terms: 15.59647396 + -13.5 = 2.09647396 x = 2.09647396 Simplifying x = 2.09647396Subproblem 2
x + 13.5 = -15.59647396 Simplifying x + 13.5 = -15.59647396 Reorder the terms: 13.5 + x = -15.59647396 Solving 13.5 + x = -15.59647396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -15.59647396 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -15.59647396 + -13.5 x = -15.59647396 + -13.5 Combine like terms: -15.59647396 + -13.5 = -29.09647396 x = -29.09647396 Simplifying x = -29.09647396Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.09647396, -29.09647396}
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