Question

How do you solve this equation using the square root property `(x + 5)^2 = 36`?

Answer 1

The solutions are
`color(blue)(x=1, x=-11`

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+5)^2)=sqrt(36`

(`sqrt36= color(blue)(+-6`)

So,
`sqrt((x+5)^2)=color(blue)(+-6`

`(x+5)=color(blue)(+-6`

Solution 1:
`x+5 = +6`
Isolating `x`
`x+5 -color(blue)(5)= +6-color(blue)(5)`
`color(blue)(x=1`

Solution 2:
`x+5 = -6`
Isolating `x`
`x+5 -color(blue)(5)= -6-color(blue)(5)`
`color(blue)(x=-11`