Expert: Richard J. Raridon - 4/29/2007

Question
There are a few problems I need help with, hope fully you can help me, I am 24 yrs old.  I appreciate it greatly.

Solve for x
1.) 25x^2=13

2.)2(x-5)^2=3

3.)x^2+4x+4=7

solve by completing the square
4.) x^2-6x-3=0

5.) 2x^2+10x+11=0

6.) Find two consecutive positive integers such that the sum of their square is 85.

Use quadratic formula to solve equations
7.) 2x^2 - 5x =3

8.) 3x^2-2x+1=0

9.) A graden area is 30ft long and 20 ft wide a path of uniform width is set around the edge.  If the remaining area is 400ft^2, what is the width of the path?

Answer
1. x^2 = 13/25 so x = +/- (13^1/2)/5
2. (x-5)^2 = 3/2 so x-5 = +/-(3/2)^1/2 or x= 5 +/-(3/2)^1/2
3. x^2 +4x -3 = 0
can't factor so x = [-4 +/-(16+12)^1/2]/2 = -2 +/-(7^1/2)
4. add 12 to each side to get x^2-6x+9 = 12
(x-3)^2 = 12 so x-3 = +/- 2(3^1/2) or x = 3 +/-2(3^1/2)
5. can't factor so x = [-10 +/-(100-88)^1/2]/4
or x = [-5 +/-(3^1/2)/2
6. x^2 +y^2 = 85 so 2^2 +9^2 = 85
7. and 8. you can try these now.  
9. If the width of the path = x, then
600 -(30-2x)(20-2x)  = 400
x^2 -25x +100 = 0 = (x-5)(x-20) so x = 5