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Simplifying 2x2 + -27x + 54 = 0 Reorder the terms: 54 + -27x + 2x2 = 0 Solving 54 + -27x + 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'. 27 + -13.5x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + -13.5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -13.5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -13.5x + x2 = 0 + -27 -13.5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -13.5x + x2 = -27 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -27 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -27 + 45.5625 Combine like terms: -27 + 45.5625 = 18.5625 45.5625 + -13.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + -6.75) equal to 4.308421985 and -4.308421985.Subproblem 1
x + -6.75 = 4.308421985 Simplifying x + -6.75 = 4.308421985 Reorder the terms: -6.75 + x = 4.308421985 Solving -6.75 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 4.308421985 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 4.308421985 + 6.75 x = 4.308421985 + 6.75 Combine like terms: 4.308421985 + 6.75 = 11.058421985 x = 11.058421985 Simplifying x = 11.058421985Subproblem 2
x + -6.75 = -4.308421985 Simplifying x + -6.75 = -4.308421985 Reorder the terms: -6.75 + x = -4.308421985 Solving -6.75 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -4.308421985 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -4.308421985 + 6.75 x = -4.308421985 + 6.75 Combine like terms: -4.308421985 + 6.75 = 2.441578015 x = 2.441578015 Simplifying x = 2.441578015Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.058421985, 2.441578015}
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