SOLUTION: Please help me solve these equations: {{{9x^2-24x+16=0 }}}. {{{x^2-3x=40 }}}.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help me solve these equations: {{{9x^2-24x+16=0 }}}. {{{x^2-3x=40 }}}.      Log On


   

Question 132911: Please help me solve these equations: 9x%5E2-24x%2B16=0+.
x%5E2-3x=40+.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



9x%5E2-24x%2B16=0 Start with the given equation

%283x-4%29%283x-4%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
3x-4=0 or 3x-4=0

x=4%2F3 or x=4%2F3 Now solve for x in each case


Since we have a repeating answer, our only answer is x=4%2F3

Notice if we graph y=9x%5E2-24x%2B16 we can see that the only root is x=4%2F3. So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+9x%5E2-24x%2B16%29+






# 2

x%5E2-3x=40+ Start with the given equation

x%5E2-3x-40=0+ Subtract 40 from both sides


%28x-8%29%28x%2B5%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-8=0 or x%2B5=0

x=8 or x=-5 Now solve for x in each case


So our answer is
x=8 or x=-5


Notice if we graph y=x%5E2-3x-40 we can see that the roots are x=8 and x=-5 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E2-3x-40%29+