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Simplifying 2x2 + 27x + -8.5 = 0 Reorder the terms: -8.5 + 27x + 2x2 = 0 Solving -8.5 + 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'. -4.25 + 13.5x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 13.5x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 13.5x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 13.5x + x2 = 0 + 4.25 13.5x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 13.5x + x2 = 4.25 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 = 4.25 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 4.25 + 45.5625 Combine like terms: 4.25 + 45.5625 = 49.8125 45.5625 + 13.5x + x2 = 49.8125 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 49.8125 Calculate the square root of the right side: 7.057797107 Break this problem into two subproblems by setting (x + 6.75) equal to 7.057797107 and -7.057797107.Subproblem 1
x + 6.75 = 7.057797107 Simplifying x + 6.75 = 7.057797107 Reorder the terms: 6.75 + x = 7.057797107 Solving 6.75 + x = 7.057797107 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 = 7.057797107 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 7.057797107 + -6.75 x = 7.057797107 + -6.75 Combine like terms: 7.057797107 + -6.75 = 0.307797107 x = 0.307797107 Simplifying x = 0.307797107Subproblem 2
x + 6.75 = -7.057797107 Simplifying x + 6.75 = -7.057797107 Reorder the terms: 6.75 + x = -7.057797107 Solving 6.75 + x = -7.057797107 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 = -7.057797107 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -7.057797107 + -6.75 x = -7.057797107 + -6.75 Combine like terms: -7.057797107 + -6.75 = -13.807797107 x = -13.807797107 Simplifying x = -13.807797107Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.307797107, -13.807797107}
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