quadratic equation

Question

Solve the quadratic equation by the square root method. Write your answers in exact form, then round to 3 decimal places. (Enter your answers as comma-separated lists.)

 

1- (3x^2)/ 2 = 6

exact answers x =
decimal answers x =

 

2-(x + 3/2) ^2 − 25 = 0

exact answers x =
decimal answers x =

 

3-(3x − 8)^2= 49

exact answers x =
decimal answers x =

 

Answer 1

I just want to work one; you should be able to pick up the method & do the others yourself.

 

#2    (x+3/2)² - 25 = 0

        (x+3/2)² = 25.  now take square root of both sides:

       (x+3/2) = ±5

         x  =  -3/2 ± 5  which is {-6.5, 3.5}

 

P.S. After your problem numbers, you have a dash in each case, which looks like a minus sign. VERY BAD PRACTICE!

Answer 2

What you have to do for these is to isolate a quantity squared on one side, then take the square root.

There may be a few more steps to finish the solution.

 

(3x^2)/ 2 = 6

3x^2 = 12

x^2 = 4

x =±2

x = -2, 2

 

(x + 3/2) ^2 − 25 = 0

(x + 3/2) ^2 = 25

x + 3/2 = ±5

Positive square root:

x +3/2 = 5

x = 5 - 3/2 = 7/2 = 3.5

Negative square root:

x +3/2 = -5
x = -5 - 3/2 = -13/2 = -6.5

x = 3.5, -6.5

 

(3x − 8)^2 = 49

(3x − 8)^2 = 49-3 = 46

3x − 8 = ±√(46)

3x = 8±√(46)

x = (8±√(46)) / 3

Use the positive and negative square root values to find the solutions.

x = 4.927, 0.406