quadratic equations: solving 3x^2 + 3x = 4

[Guest]

I SIMPLY LOVE QUADRATIC EQUATIONS!
But what happens when you don't have a perfect square root? Such as:

3x squared +3x = 4

1. You then move the 4 over by making it a -4
2. -3 plus or minus the square root of 9+48
but the square root is like 7.549834435.
something like that.

what do you do after that?
if you can help me that'd be great.

thanks,
ann.banana

 

[tkhunny]

I don't follow.

1) Try to factor it.
2) Failing that, maybe completing the square is easy enough.
3) If not, the quadratic formula will tell you the solutions.

Are you acquainted with the quadratic formula?

 

[jonboy]

Quadratic Formula: \(\displaystyle \L \;\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}\)

In which your polynomial is in the form: \(\displaystyle \L \;ax^2+bx+c=0\) and a is not equal to zero.

 

[Denis]

I SIMPLY LOVE QUADRATIC EQUATIONS!
But what happens when you don't have a perfect square root? Such as:
3x squared +3x = 4
1. You then move the 4 over by making it a -4
2. -3 plus or minus the square root of 9+48
but the square root is like 7.549834435.
something like that. what do you do after that?

1: correct; so you have 3x^2 + 3x - 4 = 0

2: first part correct; you have really:
x = [-3 +- sqrt(9 + 48)] / (2*3)
x = [-3 +- sqrt(57)] / 6
That's all; you're finished

IF you're asked to estimate x's 2 values:
x = (-3 + 7.549834435...) / 6 = .7583....
x = (-3 - 7.549834435...) / 6 = -1.7583...