Question

Solve by completing the square. q2 + 6q − 13 = 0.

Answer 1

q = 1.69, -7.69 to the nearest hundredth.

Explanation:

q^2 + 6q - 13 = 0

(q^2 + 6g + 9) - 13 - 9 = 0

(q + 3)^2 - 22 = 0

(q + 3)^2 = 22

q + 3 = +/- √22

q = √22 - 3, -√22 - 3.

q = 1.69, -7.69.

Answer 2

±
`√(22) -3`

Explanation:

we would need to first separate the -13 to complete the square. To do that we divide 6 from the 6q by 2, which is 3. We then square the 3 to get positive 9. We separate the equation to become

`q^2+6q+9-22=0`

since 9 - 22 is the same as -13

We can then reverse factor and get the equation to the form of:

`(q+3)^2-22=0`

Moving the -22 to the other side yields

`(q+3)^2=22`

Taking the square root then isolating the q gives us the answers:

`q=` ±
`√(22) -3`