Question

How do you solve this equation using the square root property `(x + 3)^2 = 49`?

Answer 1

The solutions are
`color(blue)(x=4, x=-10`

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+3)^2)=sqrt(49`

(`sqrt49= color(blue)(+-7`)

So,
`sqrt((x+3)^2)=color(blue)(+-7`

`(x+3)=color(blue)(+-7`

Solution 1:
`x+3 = +7`
Isolating `x`
`x+3 -color(blue)(3)= +7-color(blue)(3)`
`color(blue)(x=4`

Solution 2:
`x+3 = -7`
Isolating `x`
`x+3 -color(blue)(3)= -7-color(blue)(3)`
`color(blue)(x=-10`