SOLUTION: Solve the equation by completing the square. Give exact Solutions. x^2 + 4x - 21 = 0 ( X Squared plus four x Subtract twenty one

Algebra ->  Test -> SOLUTION: Solve the equation by completing the square. Give exact Solutions. x^2 + 4x - 21 = 0 ( X Squared plus four x Subtract twenty one       Log On


   

Question 106099: Solve the equation by completing the square. Give exact Solutions.

x^2 + 4x - 21 = 0
( X Squared plus four x Subtract twenty one equals zero.)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To complete the square you want to come to an equation that looks like:
%28x%2Ba%29%5E2
If you expand that form and look for common terms in your equation,
%28x%2Ba%29%5E2=x%5E2%2B2ax%2Ba%5E2
Comparing with your equation,
x%5E2%2B2ax%2Ba%5E2=x%5E2%2B4x-21%2BZ
Where Z is the constant I will add to both sides of my original equation to complete the square.
Comparing the x term,
2ax=4x
2a=4
a=2
Comparing my constant terms,
a%5E2=-21%2BZ
4=-21%2BZ
Z=25
Going back to the original equation:
x%5E2+%2B+4x+-+21+=+0
Add Z to both sides,
x%5E2%2B4x-21%2B25=+25
x%5E2%2B4x%2B4=+25
%28x%2B2%29%5E2=+25
Two solutions.
x%2B2=5%29 and x%2B2=+-5
x%2B2=5%29
highlight%28x=3%29
x%2B2=+-5
highlight%28x=-7%29
Always check your answers.
x%5E2+%2B+4x+-+21+=+0
3%5E2+%2B+4%283%29+-+21+=+0
9%2B12-21=0
0=0
Good answer.
x%5E2+%2B+4x+-+21+=+0
%28-7%29%5E2+%2B+4%28-7%29+-+21+=+0
49-28-21=0
0=0
Good answer.
x=3 and x=-7.