How do you solve #x^2+4x+1=0# by completing the square?
In addition to completing the square, use the difference of squares identity:
Hence:
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To solve the equation x^2 + 4x + 1 = 0 by completing the square, follow these steps:

Move the constant term to the other side of the equation: x^2 + 4x = 1

Take half of the coefficient of x (which is 4), square it, and add it to both sides of the equation: x^2 + 4x + (4/2)^2 = 1 + (4/2)^2 x^2 + 4x + 4 = 1 + 4

Simplify both sides of the equation: x^2 + 4x + 4 = 3

Rewrite the left side of the equation as a perfect square trinomial: (x + 2)^2 = 3

Take the square root of both sides of the equation: x + 2 = ±√3

Solve for x: x = 2 ± √3
So the solutions to the equation x^2 + 4x + 1 = 0 by completing the square are x = 2 + √3 and x = 2  √3.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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