Simplifying Expression x^2 + 10x + 16: Factoring and Quadratic Formula Analysis

x^2 + 10x + 16

To simplify the expression x^2 + 10x + 16, we can look for factors or apply the quadratic formula

To simplify the expression x^2 + 10x + 16, we can look for factors or apply the quadratic formula.

Let’s begin with factoring:

The expression can be factored as (x + 2)(x + 8).

We can verify this by expanding the factored form:

(x + 2)(x + 8) = x^2 + 8x + 2x + 16 = x^2 + 10x + 16

So, x^2 + 10x + 16 can be simplified as (x + 2)(x + 8).

Alternatively, if you prefer using the quadratic formula, we can compute the solutions for x:

The quadratic formula is x = (-b ± √(b^2 – 4ac)) / (2a)

Here, a = 1, b = 10, and c = 16.

Substituting these values into the quadratic formula:

x = (-10 ± √(10^2 – 4*1*16)) / (2*1)
x = (-10 ± √(100 – 64)) / 2
x = (-10 ± √(36)) / 2

Since the square root of 36 is 6:

x = (-10 ± 6) / 2

Now we have two possibilities:

1) x = (-10 – 6) / 2 = -16 / 2 = -8
2) x = (-10 + 6) / 2 = -4 / 2 = -2

Therefore, the solutions for x are x = -8 and x = -2.

So, after factoring, we have (x + 2)(x + 8) and after using the quadratic formula, we find that x = -8 and x = -2 are the solutions for the expression x^2 + 10x + 16.

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