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Algebra: Quadratics - Completing the Square
Express z2 + 7 z + 10 in the form ( z + a )2 + b by completing the square or otherwise :
z2 + 7 z + 10 = ( z + )2 +

tickcross


Worked Solution:

( z + a )2 = z2 + 2 a z + a2
=>( z + a )2 + b = z2 + 2 a z + a2 + b
We want to find values for a and b to make the line above into z2 + 7 z + 10
We already have the z2 term so let's look at the z term:
2a z = 7z :
For the quadratic in the question, the z coefficient is 7 which must be equal to the z term above:
=> 2 a = 7
=> a =
7
---
2
 = 3.5
a2 + b = 10 : The quadratic given has a constant term of 10
This must equal a2 + b and we now know the value of a =
7
---
2
=>a2 =
49
---
4
:
=>
49
---
4
 + b = 10
=>b =
– 9
---
4
 = –2.25

© MEI Produced by Dr Ron Knott, 23 August 2004, updated 14 May 2007
tom . button [AT] mei . org . uk 		Test reference: AlgCompleteSq.html?ref=69513,qu=cts