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Simplifying x2 + -27x + 25 = 0 Reorder the terms: 25 + -27x + x2 = 0 Solving 25 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -27x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -27x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -27x + x2 = 0 + -25 -27x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -27x + x2 = -25 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 = -25 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -25 + 182.25 Combine like terms: -25 + 182.25 = 157.25 182.25 + -27x + x2 = 157.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 157.25 Calculate the square root of the right side: 12.539936204 Break this problem into two subproblems by setting (x + -13.5) equal to 12.539936204 and -12.539936204.Subproblem 1
x + -13.5 = 12.539936204 Simplifying x + -13.5 = 12.539936204 Reorder the terms: -13.5 + x = 12.539936204 Solving -13.5 + x = 12.539936204 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 = 12.539936204 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 12.539936204 + 13.5 x = 12.539936204 + 13.5 Combine like terms: 12.539936204 + 13.5 = 26.039936204 x = 26.039936204 Simplifying x = 26.039936204Subproblem 2
x + -13.5 = -12.539936204 Simplifying x + -13.5 = -12.539936204 Reorder the terms: -13.5 + x = -12.539936204 Solving -13.5 + x = -12.539936204 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 = -12.539936204 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -12.539936204 + 13.5 x = -12.539936204 + 13.5 Combine like terms: -12.539936204 + 13.5 = 0.960063796 x = 0.960063796 Simplifying x = 0.960063796Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.039936204, 0.960063796}
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