SOLUTION: sorry to bother so confused with algebra .. (exponents pretend ^5) What solution do 2x^2 - 13x +21 = 0 and 2x^+ 9x-56 =0 have in common? Round your answer to the nearest

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Question 950449: sorry to bother so confused with algebra ..
(exponents pretend ^5)
What solution do 2x^2 - 13x +21 = 0 and 2x^+ 9x-56 =0 have in
common? Round your answer to the nearest tenth if necessary.
Found 3 solutions by josgarithmetic, macston, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Using general solution for quadratic equation.
D1 and D2 are the discriminants of each equation.


E1, D1=169-4%2A2%2A21=1

E2, D2=81%2B4%2A2%2A56=529=23%5E2

E1, x=%2813%2B-+1%29%2F4
x=12%2F4 or 14%2F4
x=3 or x=3%261%2F2

E2, x=%28-9%2B-+23%29%2F4
x=14%2F4 or x=-32%2F4
x=3%261%2F2 or x=-8

Common to both equations, highlight%283%261%2F2%29

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2+-+13x+%2B21+=+2x%5E2%2B+9x-56Subtract 2x%5E2 from each side.
-13x+21=9x-56 Add 56 to each side.
-13x+77=9x Add 13x to each side.
77=22x Divide each side by 22.
77/22=x
3.5=x ANSWER: The common solution is x=3.5.
CHECK
2x%5E2+-+13x+%2B21+=0
2%283.5%29%5E2-13%283.5%29%2B21=0
2%2812.25%29-45.5%2B21=0
24.5-45.5%2B21=0
0=0
2x%5E2%2B+9x-56=0
2%283.5%29%5E2%2B9%283.5%29-56=0%29
2%2812.25%29%2B31.5-56=0
24.5%2B31.5-56=0
0=0

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

2x%5E2+-+13x+%2B21+=+0
2x%5E2-6x+-+7x+%2B21+=+0
%282x%5E2-6x%29+-+%287x-21%29+=+0
2x%28x-3%29+-7+%28x-3%29+=+0
%28x-3%29+%282x-7%29+=+0
solutions:
x+=+3
+x+=+7%2F2=>x+=+3.5


2x%5E2%2B+9x-56+=0
2x%5E2%2B+16x-7x-56+=0
%282x%5E2%2B+16x%29-%287x%2B56%29+=0
2x%28x%2B+8%29-7%28x%2B8%29+=0
%282x-7%29+%28x%2B8%29=0
solutions:
x+=+-8
x+=+7%2F2=>x+=+3.5

both functions have one root in common and that is x+=+3.5
means, if you plug x+=+3.5 in both equations will be equal to zero, so graphs intersect in a point (3.5,0)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-60%2C+60%2C+2x%5E2+-+13x+%2B21%2C+2x%5E2%2B+9x-56%29+