Question

What are the solutions of x2 + 10x + 16 = 0?

Answer 1

x

=

−

8

,

−

2

Explanation:

Given:

x

2

+

10

x

+

16

=

0

To complete the square put the two

x

terms on the left and the constant on the right of the equation:

x

2

+

10

x

=

−

16

Complete the square by multiplying the

x

-term by

1

2

:

1

2

⋅

10

=

5

and adding the square of this number to the right side of the equation:

5

2

=

25

(

x

+

5

)

2

=

−

16

+

25

UNDERSTANDING CHECK:

(

x

+

5

)

2

=

x

2

+

10

x

+

25

.

The

+

25

was not in the original equation. If we add

+

25

to one side of the equation, we must add the same amount to the other side of the equation to keep it balanced.

(

x

+

5

)

2

=

9

To solve, square root both sides of the equation:

√

(

x

+

5

)

2

=

±

√

9

x

+

5

=

±

3

x

=

−

5

±

3

x

=

−

5

+

3

=

−

2

,

x

=

−

5

−

3

=

−

8

x

=

−

8

,

−

2

Answer 2

The answer is -2,-8