How do you solve the equation (3x+2)^2-49=0?

2 Answers
Shwetank Mauria
Feb 19, 2017

x=5/3 and x=-3

Explanation:

(3x+2)^2-49=0 can be written as

(3x+2)^2-7^2=0

As a^2-b^2 can be factorized as (a+b)(a-b), this can be factorized as

(3x+2+7)(3x+2-7)=0

Hence, either 3x+2+7=0 i.e. 3x=-9 and x=-3

or 3x+2-7=0 i.e. 3x=7-2=5 and x=5/3

Astralboy
Feb 19, 2017

Alternative to get x=5/3 and x=-3

Explanation:

You can also treat this as a completing the square problem where the step of making the square is already done for you.

Move the 49 to the other side:

(3x+2)^2=49

Square root both sides:

3x+2=(+/-)7

Treat it as two problems and solve for x

3x+2=7

3x=5

x=5/3

That's the first answer

3x+2=-7

3x=-9

x=-3

That's the second answer.

Related questions
See all questions in Use Square Roots to Solve Quadratic Equations
Impact of this question
4933 views around the world
You can reuse this answer
Creative Commons License