SOLUTION: Factoring to solve Quadratic Equations. Solve by Factoring. 1. x squared + 7x = 8 2. x squared = 25 3. 2t squared + 8t - 64 =0 4. 3a squared - 36a + 81 = 0 5. 2a sq

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factoring to solve Quadratic Equations. Solve by Factoring. 1. x squared + 7x = 8 2. x squared = 25 3. 2t squared + 8t - 64 =0 4. 3a squared - 36a + 81 = 0 5. 2a sq      Log On


   

Question 115480: Factoring to solve Quadratic Equations.
Solve by Factoring.
1. x squared + 7x = 8
2. x squared = 25
3. 2t squared + 8t - 64 =0
4. 3a squared - 36a + 81 = 0
5. 2a squared - a - 21 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first few to give you an idea how to do these

#1

x%5E2%2B7x=8 Start with the given equation


x%5E2%2B7x-8=0 Move all of the terms to the left side


%28x%2B8%29%28x-1%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%2B8=0 or x-1=0

x=-8 or x=1 Now solve for x in each case


So our answer is
x=-8 or x=1


Notice if we graph y=x%5E2%2B7x-8 we can see that the roots are x=-8 and x=1 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E2%2B7x-8%29+




#2

x%5E2=25 Start with the given equation


x%5E2-25=0 Move all of the terms to the left side


%28x%2B5%29%28x-5%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%2B5=0 or x-5=0

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


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


Notice if we graph y=x%5E2-25 we can see that the roots are x=-5 and x=5 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E2-25%29+



#3


2t%5E2%2B8t-64=0 Start with the given equation


2%28t%5E2%2B4t-32%29=0 Factor out the GCF 2

2%28t%2B8%29%28t-4%29=0 Factor the inner expression (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
t%2B8=0 or t-4=0

t=-8 or t=4 Now solve for t in each case


So our answer is
t=-8 or t=4


Notice if we graph y=2t%5E2%2B8t-64 we can see that the roots are t=-8 and t=4 . So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+2x%5E2%2B8x-64%29+