SOLUTION: solve. a)x^2 - 2x=15 b)3x^2+19+1=0 c)1/4x +12 - 1/x^2-9=5/x-3 thank you so much.

Algebra ->  Expressions-with-variables -> SOLUTION: solve. a)x^2 - 2x=15 b)3x^2+19+1=0 c)1/4x +12 - 1/x^2-9=5/x-3 thank you so much.      Log On


   

Question 63348: solve. a)x^2 - 2x=15 b)3x^2+19+1=0 c)1/4x +12 - 1/x^2-9=5/x-3
thank you so much.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve.
:
a)x^2 - 2x = 15
:
Subtract 15 to both sides, we have simple quadratic equation, we can factor:
x^2 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x = +5
and
x = -3
:
Substituting either solution in the original equation will prove our solutions
:
:
b)3x^2 + 19 + 1 = 0
3x^2 + 20 = 0
:
Subtract 20 from both sides:
3x^2 = -20
:
Divide both sides by 3
x^2 = -20/3
x = +/- SqRt(-20/3)
x =+/- SqRt((5*4*-1)/3)
:
Extract the SqRt(4) and i (sqRt of -1):
x = +/- 2i*SqRt(5/3)
:
:
:
c)1%2F%284x%2B12%29+-+1%2F%28x%5E2-9%29+=++5%2F%28x-3%29
:
Factor where we can:
1%2F%284%28x%2B3%29%29+-+1%2F%28%28x-3%29%28x%2B3%29%29+=++5%2F%28x-3%29
:
We can see the common denominator is 4(x+3)(x-3), mult eq by that and we get:
1(x-3) - 4(1) = 4(x+3)*5
x - 3 - 4 = 20x + 60
x - 7 = 20x + 60
x - 20x = 60 + 7
-19x = + 67
x = -67/19