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Simplifying x2 + -2x + -27 = 0 Reorder the terms: -27 + -2x + x2 = 0 Solving -27 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -2x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -2x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2x + x2 = 0 + 27 -2x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -2x + x2 = 27 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 27 + 1 Reorder the terms: 1 + -2x + x2 = 27 + 1 Combine like terms: 27 + 1 = 28 1 + -2x + x2 = 28 Factor a perfect square on the left side: (x + -1)(x + -1) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -1) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -1 = 5.291502622 Simplifying x + -1 = 5.291502622 Reorder the terms: -1 + x = 5.291502622 Solving -1 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.291502622 + 1 x = 5.291502622 + 1 Combine like terms: 5.291502622 + 1 = 6.291502622 x = 6.291502622 Simplifying x = 6.291502622Subproblem 2
x + -1 = -5.291502622 Simplifying x + -1 = -5.291502622 Reorder the terms: -1 + x = -5.291502622 Solving -1 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.291502622 + 1 x = -5.291502622 + 1 Combine like terms: -5.291502622 + 1 = -4.291502622 x = -4.291502622 Simplifying x = -4.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.291502622, -4.291502622}
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