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Simplifying x2 + -27x + 100 = 0 Reorder the terms: 100 + -27x + x2 = 0 Solving 100 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -27x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -27x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -27x + x2 = 0 + -100 -27x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -27x + x2 = -100 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 = -100 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -100 + 182.25 Combine like terms: -100 + 182.25 = 82.25 182.25 + -27x + x2 = 82.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -13.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -13.5 = 9.069178574 Simplifying x + -13.5 = 9.069178574 Reorder the terms: -13.5 + x = 9.069178574 Solving -13.5 + x = 9.069178574 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 = 9.069178574 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 9.069178574 + 13.5 x = 9.069178574 + 13.5 Combine like terms: 9.069178574 + 13.5 = 22.569178574 x = 22.569178574 Simplifying x = 22.569178574Subproblem 2
x + -13.5 = -9.069178574 Simplifying x + -13.5 = -9.069178574 Reorder the terms: -13.5 + x = -9.069178574 Solving -13.5 + x = -9.069178574 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 = -9.069178574 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -9.069178574 + 13.5 x = -9.069178574 + 13.5 Combine like terms: -9.069178574 + 13.5 = 4.430821426 x = 4.430821426 Simplifying x = 4.430821426Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.569178574, 4.430821426}
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