Question

How do you solve this equation using the square root property `(x + 7)^2 = 81`?

Answer 1

The solutions are
`color(blue)(x=2,x=-16`

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+7)^2)=sqrt(81`

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

So,
`sqrt((x+7)^2)=color(blue)(+-9`

`(x+7)=color(blue)(+-9`

Solution 1:
`x+7 = +9`
Isolating `x` completely:
`x+7 -color(blue)(7) = +9 -color(blue)(7)`
`color(blue)(x=2`

Solution 2:
`x+7 = -9`
Isolating `x` completely:
`x+7-color(blue)(7) = -9-color(blue)(7)`
`color(blue)(x=-16`