Question

How do you use the square root property to solve this equation `(2x+3)^2 = 25`?

Answer 1

The solutions are
`color(blue)(x=1,x=-4`

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((2x+3)^2)=sqrt(25`

(`sqrt25= color(blue)(+-5`)

So,
`sqrt((2x+3)^2)=color(blue)(+-5`

`(2x+3)=color(blue)(+-5`

Solution 1:
`2x+3 = +5`
Isolating `x`
`2x+3 -color(blue)(3)= +5-color(blue)(3)`
`2x=2`
`color(blue)(x=1`

Solution 2:
`2x+3 = -5`
Isolating `x`
`2x+3 -color(blue)(3)= -5-color(blue)(3)`
`2x=-8`
`color(blue)(x=-4`