what is the positive solution of the equation x^2=2x+35? solve by factoring.

Question

its a word problem kinda but i don't know what techique to use in algebra 2.

Answer 1

x²-2x-35=0

(x-7)(x+5) = 0

x=7 or -5

so the positive solution is x=7

Answer 2

Solve by factoring:    x^2=2x+35

 

First, get everything on one side and 0 on the other side of the equation:

      x^2-2x+35 = 0

 

Now, remember F-O-I-L (First-Outside-Inside-Last).

  (x+a)(x+b) = x^2 + bx + ax + ab

  (x+a)(x+b) = x^2 + (a+b)x + ab

We want to find (a+b)=-2 and ab=35.  Those two numbers are a=5 and b=-7 (check it out!)

 

That makes the equation:  (x+5)(x-7)=0

   Either x=-5 or x=7.        [If the product equals 0, one or both terms must equal 0]

  The positive solution is x=7.