Hi cleanncrazi,
Here are the answers to your questions:
1. 2m^2+10m=-12
2m^2+10m+12=0
m^2+5m+6=0
(m+3)(m+2)=0
m=-3 and m=-2
2. (a-2)(a-3)=6
a^2-3a-2a+6=6
a^2-5a=0
a(a-5)=0
a-5=0
a=5
3. 3/x+5/3x=1
3/x+5/3x-1=0
3(3x)+5(x)-1(x)(3x)=0
9x+5x-3x^2=0
-3x^2+14x=0
x(-3x+14)=0
-3x=-14
x=14/3
4. 3/t-3=5/t+4
(3-3t)/t=(5+4t)/t
0= 5+4t-3+3t
0=2+7t
-2=7t
-2/7=t
5. m=r/1+rt for r (assuming this is meant to be m=r/(1+rt)
m+rtm=r
m=r-rtm
m=r(1-tm)
m/(1-tm)=r
6. 3sqrtx+5=12
9(x+5)=144
x+5=16
x=11
7. (square root) x^2+3x+6=4
x^2+3x+6=4^2
x^2+3x+6=16
x^2+3x-10=0
(x+5)(x-2)=0
x=-5, x=2
8. x^2-2x-24=0
(x+6)(x+4)=0
x=6, x=4
9. 2x^2+7x=4
2x^2+7x-4=0
(x+4)(2x-1)=0
x=-4, x=1/2
10. x^2-5x-6=0
x=-[(-5)+-sqrt[(-5)^2-4(1)(6)]]/2
x=[5+-sqrt(25+24)]/2
x=[5+-sqrt(49)]/2
x1=[5+sqrt(49)]/2
x1=(5+7)/2
x1=6
x2=[5-sqrt(49)]/2
x2=(5-7)/2
x2=-1
Questions 1, 8, and 9 were done using the simple factoring method as
demonstrated at the following link:
Purplemath - Factoring Quadratics Lesson - 1
http://www.purplemath.com/modules/factquad.htm
I hope this helps! If you have any questions please feel free to ask
for clarification.
Regards,
Deadlychiapet |