# How do you factor and solve #x^2+4x+4=0 #?

Let's factorise this equation using the middle-term break:

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To factor and solve the equation (x^2 + 4x + 4 = 0), you can use the quadratic formula.

First, identify the coefficients (a), (b), and (c) in the quadratic equation (ax^2 + bx + c = 0):

(a = 1), (b = 4), (c = 4)

Then, substitute these values into the quadratic formula:

[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}]

Substitute the values of (a), (b), and (c):

[x = \frac{{-4 \pm \sqrt{{(4)^2 - 4(1)(4)}}}}{{2(1)}}]

Simplify under the square root:

[x = \frac{{-4 \pm \sqrt{{16 - 16}}}}{{2}}]

[x = \frac{{-4 \pm \sqrt{{0}}}}{{2}}]

Since the square root of 0 is 0:

[x = \frac{{-4 \pm 0}}{{2}}]

Simplify further:

[x = \frac{{-4}}{{2}}]

[x = -2]

Therefore, the equation (x^2 + 4x + 4 = 0) has one real root, which is (x = -2). This also means that the quadratic expression (x^2 + 4x + 4) can be factored as ((x + 2)(x + 2)), which further simplifies to ((x + 2)^2).

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To factor and solve the equation (x^2 + 4x + 4 = 0), follow these steps:

- Identify the coefficients of the quadratic equation: (a = 1), (b = 4), and (c = 4).
- Use the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}).
- Substitute the values of (a), (b), and (c) into the quadratic formula.
- Calculate the discriminant, (b^2 - 4ac).
- If the discriminant is positive, there are two real roots. If it's zero, there is one real root (a repeated root). If it's negative, there are two complex roots.
- Substitute the discriminant and other values into the quadratic formula to find the roots.

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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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