Square Root 5x+84 = 3x+28. Solve the equation.

Question

The 5x+84 is square rooted. I am aware that the answer is -7.Just don't know how to work it

Answer 1

√(5x + 84) = 3x + 28

 

5x + 84 = (3x + 28)²

 

5x + 84 = 9x² + 168x + 784

 

0 = 9x² + 163x + 700

 

0 = (x + 7)(9x + 100)

 

x = -7 or -100/9

 

However plugging in x =  -100/9 gives:

 

√(5x + 84) = √(-500/9 + 84) = √(256/9) = 16/3

 

3x + 28 = -100/3 + 28 = -16/3

 

So -100/9 is extraneous.

 

The solution x = -7 is the only one that works:

 

√(5x + 84) = √(-35 + 84) = √49 = 7

 

3x + 28 = -21 + 28 = 7