Question

find the value of c that completes the square

I don't understand why the answer is 121/256

z^2+ 11/8 z + c



Thanks!

Answer 1

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Remark:

( a + b )² = a² + 2 ∙ a ∙ b + b²
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In this case:

( z + b )² = z² + 2 ∙ z ∙ b + b²

( z + b )² = z² + 11 z / 8 + b²

2 ∙ z ∙ b = 11 z / 8

Divide both sides by z

2 b = 11 / 8

Divide both sides by 2

b = 11 / 16


b² = ( 11 / 16 )²

b² = 11² / 16 ²

b² = 121 / 256


( z + 11 / 16 )² = z² + 11 z / 8 + 121 / 256