Question

How do you solve `(x + 4)^2 = 81` using the square root property?

Answer 1

The solutions are
`color(blue)(x=5, x=-13`

Explanation:

The square root property involves taking the square root of both the terms on either side of the equation.

Applying the same to the given equation:

`sqrt((x+4)^2)=sqrt(81`

(`sqrt81= color(blue)(+-9`)

So,
`sqrt((x+4)^2)=color(blue)(+-9`

`(x+4)=color(blue)(+-9`

Solution 1:
`x+4 = +9`
Isolating `x`
`x+4 -color(blue)(4)= +9-color(blue)(4)`
`color(blue)(x=5`

Solution 2:
`x+4 = -9`
Isolating `x`
`x+4 -color(blue)(4)= -9-color(blue)(4)`
`color(blue)(x=-13`