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Simplifying x2 + -27x + 9 = 0 Reorder the terms: 9 + -27x + x2 = 0 Solving 9 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -27x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -27x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -27x + x2 = 0 + -9 -27x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -27x + x2 = -9 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 = -9 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -9 + 182.25 Combine like terms: -9 + 182.25 = 173.25 182.25 + -27x + x2 = 173.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 173.25 Calculate the square root of the right side: 13.162446581 Break this problem into two subproblems by setting (x + -13.5) equal to 13.162446581 and -13.162446581.Subproblem 1
x + -13.5 = 13.162446581 Simplifying x + -13.5 = 13.162446581 Reorder the terms: -13.5 + x = 13.162446581 Solving -13.5 + x = 13.162446581 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 = 13.162446581 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.162446581 + 13.5 x = 13.162446581 + 13.5 Combine like terms: 13.162446581 + 13.5 = 26.662446581 x = 26.662446581 Simplifying x = 26.662446581Subproblem 2
x + -13.5 = -13.162446581 Simplifying x + -13.5 = -13.162446581 Reorder the terms: -13.5 + x = -13.162446581 Solving -13.5 + x = -13.162446581 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 = -13.162446581 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.162446581 + 13.5 x = -13.162446581 + 13.5 Combine like terms: -13.162446581 + 13.5 = 0.337553419 x = 0.337553419 Simplifying x = 0.337553419Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.662446581, 0.337553419}
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