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Simplifying x2 + -27x + 49 = 0 Reorder the terms: 49 + -27x + x2 = 0 Solving 49 + -27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -27x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -27x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -27x + x2 = 0 + -49 -27x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -27x + x2 = -49 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 = -49 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -49 + 182.25 Combine like terms: -49 + 182.25 = 133.25 182.25 + -27x + x2 = 133.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 133.25 Calculate the square root of the right side: 11.543396381 Break this problem into two subproblems by setting (x + -13.5) equal to 11.543396381 and -11.543396381.Subproblem 1
x + -13.5 = 11.543396381 Simplifying x + -13.5 = 11.543396381 Reorder the terms: -13.5 + x = 11.543396381 Solving -13.5 + x = 11.543396381 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 = 11.543396381 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 11.543396381 + 13.5 x = 11.543396381 + 13.5 Combine like terms: 11.543396381 + 13.5 = 25.043396381 x = 25.043396381 Simplifying x = 25.043396381Subproblem 2
x + -13.5 = -11.543396381 Simplifying x + -13.5 = -11.543396381 Reorder the terms: -13.5 + x = -11.543396381 Solving -13.5 + x = -11.543396381 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 = -11.543396381 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -11.543396381 + 13.5 x = -11.543396381 + 13.5 Combine like terms: -11.543396381 + 13.5 = 1.956603619 x = 1.956603619 Simplifying x = 1.956603619Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.043396381, 1.956603619}
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