SOLUTION: Dear Tutor, Please help me solve this tedious math problem. Your help is GREATLY appreciated. Thanks so much!!! :) By the way, I need to solve by factoring the square 4

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Dear Tutor, Please help me solve this tedious math problem. Your help is GREATLY appreciated. Thanks so much!!! :) By the way, I need to solve by factoring the square 4      Log On


   

Question 220853: Dear Tutor,
Please help me solve this tedious math problem. Your help is GREATLY appreciated. Thanks so much!!! :)

By the way, I need to solve by factoring the square
4x^2-4x-99=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2+-+4x+-+99+=+0
First divide both sides by 4
x%5E2+-+x+-+99%2F4+=+0
Now add 99%2F4 to both sides
x%5E2+-+x+=+99%2F4
Now take 1/2 of the coefficient of x
which is -1, square it, and add it to
both sides
x%5E2+-+x+%2B+%28-1%2F2%29%5E2+=+99%2F4+%2B+%28-1%2F2%29%5E2
x%5E2+-+x+%2B+1%2F4+=+99%2F4+%2B+1%2F4
x%5E2+-+x+%2B+1%2F4+=+100%2F4
Notice that both sides are perfect squares
%28x+-+1%2F2%29%5E2+=+%2810%2F2%29%5E2
I'll take the square root of both sides
x+-+1%2F2+=+10%2F2
x+=+10%2F2+%2B+1%2F2
x+=+11%2F2
There is also a negative square root
x+-+1%2F2+=+-10%2F2
x+=+-9%2F2
The roots are x+=+11%2F2 and x+=+-9%2F2
I'll plot it to verify
+graph%28+600%2C+600%2C+-10%2C+10%2C+-110%2C+5%2C+4x%5E2+-+4x+-+99%29+
Looks about right