Need help with solving quadratics with square roots

Question

I need help with these, if someone could explain them step-by-step, I would really appreciate it :)

1. 3x² - 48 = 0
2. x² = 36
3. p² - 50 = 0

Answer 1

In order to find x (or p), you must isolate it on the left side of the equation.  [note: this is what it means to "solve" for x]

 

The reverse operation is applied to both sides of the equation.  That is, if the expression has a subtraction, then perform an addition of the same amount and the value goes to the other side.

 

Remember that √x² = ±x

 

 

1.  3x² - 48 = 0

     3x² = 48             [add 48 to both sides]

      x² = 16             [divide both sides by 3]

      x = ±4             [take the square root of each side]

 

2.  x² = 36

     x = ±6             [take square root of each side]

 

3.  p² - 50 = 0

     p² = 50

     p = ±√50

 

     Now, note that 50 has prime factors of 2*5*5, so √50 = √(2*2*5) = 5√2