complet the square using the square root property

You made an typing error when you were posting the problem, but I think the problem you are looking to solve for is as follows: x^{2} + 10x + 25 = 16

Note that we need to factor the left hand side of the equation in such a way that we get a product of two identical binomials (i.e., a perfect square).

Recall that to complete the square we use the following formula: (b/2)^{2}

In this problem b=10, so (b/2)^{2} = (10/2)^{2} = (5)^{2}

This tells us that the left hand side of the original equation factors into (x + 5)^{2}. That is,

x^{2} + 10x + 25 = 16

(x + 5)(x + 5) = 16

(x + 5)^{2} = 16

Now, take the square root of both sides of the equation:

√(x + 5)^{2} = √16

(x + 5) = ± 4

x + 5 = ± 4

Subtract 5 from both sides of the equation to solve for x:

x + 5 = ± 4

- 5 - 5

______________

x = -5 ± 4 ==> x = -5 + 4 and x = -5 - 4

x = -5 + 4 = -1

x = -5 - 4 = -9

Thus, x = -1 and x = -9