SOLUTION: what is the answer step by step to the following quadratic equations ? x squared-4x-15=0 x squared+8x-33=0 x squared+5x+2=0 3xsquared-3x+6=0 Help would be great i need it bad

Question 120709: what is the answer step by step to the following quadratic equations ?
x squared-4x-15=0
x squared+8x-33=0
x squared+5x+2=0
3xsquared-3x+6=0
Help would be great i need it bad
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
what is the answer step by step to the following quadratic equations ?
:
These need to be solved using the quadratic formula, which is:

:
x^2 - 4x - 15 = 0
In this problem a = 1; b =-4; c =-15; substitute these value in the quad formula

; remember minus a minus is a plus

; find the square root of 76 with a calc
Two solutions
Solution 1:

x = 6.3589 is solution 1
Solution 2:

x = -2.3589 is solution 2
:
:
x^2 + 8x - 33 = 0
In this problem a = 1; b = 8; c =-33, substitute these in the quad formula

Solution 1

x = 3 is solution 1
Solution 2

x = -11 is solution 2
:
Note that these solutions are both integers, so we could have just factored
(x+11)(x-3)= 0 would have saved a lot of time
:
:
x^2 + 5x + 2 = 0
You should be getting the hang of it now

:
Do the math on this one just like we did on the 1st two
:
You should get: x = -4.56 and x = -.438, (neither comes out even)
:
:
This one is a special case, does not have any real roots
we shall see why as we proceed with the quad formula
3x^2 - 3x + 6 = 0

we have a square root of a negative number so there is no real roots
:
Look up the word "discriminant" in the index of your algebra book.
This is related to what we just did.
:
Did this make sense to you. It's very important that you understand exactly what's going on here. Do you have any questions?
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