Question

Helen is solving a quadratic equation. She wants to find the value of x by taking the square root of both sides of the equation. Which equation allows her to do this?

1) x^2+ 24x + 144 = 17

2) x^2 + 7x + 12 = 34

3) x^2+ 7x + 49 = 10

4) x^2+ 25x + 10 = 20

Answer 1

1)
`x^2+ 24x + 144 = 17`

Explanation:

The answer is 1) because the left side in the equation

`x^2+ 24x + 144 = 17`

can be represented a perfect square:

`x^2+ 24x + 144=(x+12)^2`

so we have that the original equation becomes:

`(x+12)^2=17`

and then, taking the square root of both sides of the equation:

`√((x+12)^2) =` ±
`√(17)`

`x+12=` ±
`√(17)`

we are left with an equation where we can find the values of x.

so we clear for x and we get:

`x=` ±
`√(17)`
`-12`

thus, the two values of x are:

`x_(1)=√(17)-12 \\x_(2)=-√(17)-12`