nicole and adam are each saving money for a car. the total amount of money nicole will save is represented by the function f(x)=36+4x. the total amount of money adam will save is represented by the function g(x)=x^2+15. after how many weeks, x, will they have the same amount of money saved? explain.

They will have the same amount of money after 7 weeks.

We first set these equal to each other:
36+4x=x²+15

We want to gather all of the variables on one side.  Subtract 4x from both sides:
36+4x-4x=x²+15-4x
36=x²-4x+15

We want the equation to be equal to 0 to solve it, so subtract 36 from both sides:
36-36=x²-4x+15-36
0=x²-4x-21

We can factor this expression.  We want factors of -21 that sum to -4; -7(3)=-21 and -7+3=-4:
0=(x-7)(x+3)

Using the zero product property, we know that x-7=0 or x+3=0; this means x=7 or x=-3.  Since a negative number of weeks makes no sense, the answer is 7 weeks.