Transcript Document

Solving Quadratics
and Exact Values
Solving Quadratic Equations by Factoring
ax2  bx  c  0
ok
ok
2
Let's solve the equation 1 x  7 x
-18
 18
need this
to be 0
-18
First you need to get it in what we call "quadratic form"
which means
2
ax  bx  c  0
x  7 x  18  0
x  9x  2  0
x  9  0 or x  2  0
So we have
2
x  9 or x  2
Now let's factor the
left hand side
Now set each factor = 0 and
solve for each answer.
Extracting Square Roots
The idea behind this method is when you have
some "stuff" squared that you can get by itself
on the left hand side of the equation (no other
variables on the right hand side), you can then
take the square root of each side to cancel out
the square.
Get the "squared stuff" alone
which in this case is the t 2
25
5t  125
2
5
5
square root each side. Since you loose
t  2525 Now
any negative sign when you square something,
2
t  5
both the + and – of the number would solve
the equation so you must do both.
Let's try another one
Get the "squared stuff" alone
which in this case is the u 2
49
49
uu 
44
49
2
u 
4
22
4u  49
2
4
4
Now square root each side and
DON'T FORGET BOTH THE + AND –
Remember with a fraction you can square
root the top and square root the bottom
7
u
2
Another Example
Get the "squared stuff" alone
which in this case is the stuff in the
brackets and it is alone.
2x 1
2

50
2 x  1  5 2
DON'T FORGET BOTH THE +
AND –
Let's simplify the Surd
Now solve for x
-1
2 x  1  5 2
2
 50
Now square root each side and
25 × 2
-1
2x 1
2
2
 1 5 2
x
2
One Last Example
Get the "squared stuff" alone
which in this case is the stuff in the
brackets.
2 y  3
2
  25
2 y  3   5i
+3
+3
 25  0
-25
2
-25
Now square root each side and
DON'T FORGET BOTH THE +
AND –
This will give you an i
Year 12 Calculus 
Now solve for y
2 y  3  5i
2
2 y  3
2
3  5i
y
2
Acknowledgement
I wish to thank Shawna Haider from Salt Lake Community College, Utah
USA for her hard work in creating this PowerPoint.
www.slcc.edu
Shawna has kindly given permission for this resource to be downloaded
from www.mathxtc.com and for it to be modified to suit the Western
Australian Mathematics Curriculum.
Stephen Corcoran
Head of Mathematics
St Stephen’s School – Carramar
www.ststephens.wa.edu.au