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Simplifying -0.05x2 + 2.7x + 5.5 = 0 Reorder the terms: 5.5 + 2.7x + -0.05x2 = 0 Solving 5.5 + 2.7x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -110 + -54x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + -54x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + -54x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -54x + x2 = 0 + 110 -54x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 -54x + x2 = 110 The x term is -54x. Take half its coefficient (-27). Square it (729) and add it to both sides. Add '729' to each side of the equation. -54x + 729 + x2 = 110 + 729 Reorder the terms: 729 + -54x + x2 = 110 + 729 Combine like terms: 110 + 729 = 839 729 + -54x + x2 = 839 Factor a perfect square on the left side: (x + -27)(x + -27) = 839 Calculate the square root of the right side: 28.965496716 Break this problem into two subproblems by setting (x + -27) equal to 28.965496716 and -28.965496716.Subproblem 1
x + -27 = 28.965496716 Simplifying x + -27 = 28.965496716 Reorder the terms: -27 + x = 28.965496716 Solving -27 + x = 28.965496716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = 28.965496716 + 27 Combine like terms: -27 + 27 = 0 0 + x = 28.965496716 + 27 x = 28.965496716 + 27 Combine like terms: 28.965496716 + 27 = 55.965496716 x = 55.965496716 Simplifying x = 55.965496716Subproblem 2
x + -27 = -28.965496716 Simplifying x + -27 = -28.965496716 Reorder the terms: -27 + x = -28.965496716 Solving -27 + x = -28.965496716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = -28.965496716 + 27 Combine like terms: -27 + 27 = 0 0 + x = -28.965496716 + 27 x = -28.965496716 + 27 Combine like terms: -28.965496716 + 27 = -1.965496716 x = -1.965496716 Simplifying x = -1.965496716Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.965496716, -1.965496716}
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