SOLUTION: Can you please help show me how to solve this quadratic equation by completing the square. w^2 - 5w = 14 Thank you so much

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can you please help show me how to solve this quadratic equation by completing the square. w^2 - 5w = 14 Thank you so much      Log On


   

Question 170891: Can you please help show me how to solve this quadratic equation by completing the square.
w^2 - 5w = 14
Thank you so much
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
w%5E2+-+5w+=+14
f%28w%29=%28w%5E2-5w%29-14
Complete the square by adding 6-1/4:
f%28w%29=%28w%5E2-5w%2B6%281%2F4%29%29highlight%28-6%281%2F4%29%29-14 ---> Remember to subtract 6-1/4 too so the value of the expression does not change.
f%28w%29=%28w-2%281%2F2%29%29%5E2-highlight%28%2825%2F4%29%29-14 ----> convert to improper fractions so it's easier to deal with.
, ANSWER
You know what, it follows "vertex-form" for a quadratic function:
f%28x%29=a%28x-h%29%5E2%2Bk ---> x=w
We have, h=2%281%2F2%29, & k=%28-81%2F4%29 --> VERTEX POINTS
Let's see the graph below:
---> see vertex (2-1/2,-81/4)
.
Let's see the x-intercepts:
w=x ---> x%5E2-5x-14=0
where----->system%28a=1%2Cb=-5%2Cc=-14%29
By Quadratic Eqn: x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x=%28-%28-5%2B-sqrt%28-5%5E2-4%2A1%2A-14%29%29%29%2F%282%2A1%29
x=%285%2B-sqrt%2825%2B56%29%29%2F2=%285%2B-sqrt%2881%29%29%2F2=%285%2B-9%29%2F2
x=%285%2B9%29%2F2=14%2F2=highlight%287%29
x=%285-9%29%2F2=-4%2F2=highlight%28-2%29
See again the graph:
---> see the x-intercepts (-2,0) & (7,0).It's good!
Thank you,
Jojo