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# x^2+10x=25=16

complet the square using the square root property

### 1 Answer by Expert Tutors

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)
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