How do you solve #x^2+4x+1=0# by completing the square?

Answer 1

#x=-2+-sqrt(3)#

In addition to completing the square, use the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#
with #a=(x+2)# and #b=sqrt(3)# as follows:
#0 = x^2 + 4x + 1#
#=(x+2)^2-4+1#
#=(x+2)^2-3#
#=(x+2)^2-(sqrt(3))^2#
#=((x+2)-sqrt(3))((x+2)+sqrt(3))#
#=(x+2-sqrt(3))(x+2+sqrt(3))#

Hence:

#x = -2+-sqrt(3)#
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Answer 2

To solve the equation x^2 + 4x + 1 = 0 by completing the square, follow these steps:

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

  2. 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

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

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

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

  6. 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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Answer from HIX Tutor

When evaluating a one-sided 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 one-sided 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 one-sided 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 one-sided 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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