SOLUTION: Use factoring to solve the equation. 9 x^ 2 + 45 x = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use factoring to solve the equation. 9 x^ 2 + 45 x = 0       Log On


   

Question 113952: Use factoring to solve the equation.
9 x^ 2 + 45 x = 0

Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9+x%5E+2+%2B+45+x+=+0+ Start with the given equation

9x%28x%2B5%29=0 Factor the left side


Now set each factor equal to zero:

9x=0 or x%2B5=0

x=0 or x=-5 Now solve for x in each case


So our solutions are x=0 or x=-5

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

9+x%5E+2+%2B+45+x+=+0........ each term in the expression has a common factor of 9x, and we can simply factor out an 9x:
9+x%28x+%2B+5%29+=+0........ ....now we have a product of an monomial and an binomial equal to 0
the product is equal to 0 if one or both factors are equal to 0
so
if 9x=0 then 9+x%28x+%2B+5%29+=+0
it will be true only if x=0; notice that 9 is not equal to 0
so x=0 is first solution
then
if %28x+%2B+5%29+=+0,9+x%28x+%2B+5%29 will be equal to +0 too
x+%2B+5+=+0 only if x+=+-5
so
x+=+-5..........another solution

check both solutions:
9+x%5E+2+%2B+45+x+=+0........ plug in x=0
9+%2A0%5E+2+%2B+45+%2A0+=+0
0+%2B+0+=+0
0++=+0

9+x%5E+2+%2B+45+x+=+0........ plug in x+=+-5
9+%2A%28-5%29%5E+2+%2B+45+%2A%28-5%29+=+0
9%2A25+-+225=+0
225+-+225+=+0
0+=+0