Solve x² + 4x - 1 = 0 by completing the square

Solve the quadratic equation by completing the square:
​x² + 4x - 1 = 0

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To get started, add 1 to each side.

x² - 4x - 1 = 0 {original equation}
x² - 4x = 1 {added 1 to each side}

Then, take half of the coefficient of x, square it, and add it to both sides.

x² - 4x + 2² = 1 + 2² {took half of the coefficient of x, squared it, and added to both sides}
x² - 4x + 4 = 1 + 4 {evaluated exponents}
x² - 4x + 4 = 5 {combined like terms on the right side}
(x - 2)² = 5 {factored the left side}
x - 2 = ±√5 {took the square root of each side}
x = 2 ± √5 {subtracted 2 from each side}

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