SOLUTION: If a number is added to its square, the sum is 156. Find the number. & One number is 3 less than twice another number. The product of the two numbers is 5. Find the number

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: If a number is added to its square, the sum is 156. Find the number. & One number is 3 less than twice another number. The product of the two numbers is 5. Find the number      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 31622: If a number is added to its square, the sum is 156. Find the number.
&
One number is 3 less than twice another number. The product of the two numbers is 5. Find the numbers.
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
a number = x
the number squared = x^2
+x%5E2+%2B+x+=+156+
+x%5E2%2Bx-156=0+ Factor
+%28x-12%29%28x%2B13%29=0+
+x-12=0+ or +x%2B13=0+
+x=12+ or +x=-13+
NEXT
m*n=5
m=2n-3
Substitute the second equation into the first
+%282n-3%29n=5+ distribute the n
+2n%5E2+-3n+=5+ subtract 5
+2n%5E2+-3n+-5+=0+ factor
+%282n-5%29%28n%2B1%29=0+
+2n-5=0+ or+n%2B1=0+
+n=5%2F2+ or +n=-1+
plug each one of these back into the first equation
+m%2An=5+ or +m%2An=5+
+m%2A%285%2F2%29=5+ or +m%2A%28-1%29=5+
+m+=5%282%2F5%29+ or +m=-5+
+m=2+ or +m=-5+
so your soultions are:
5/2 and 2
OR
-1 and -5