x^2+10x=25=16

Question

complet the square using the square root property

Answer 1

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:     x² + 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,

          x² + 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