Rewrite each expression by completing the square.

a. z^2 - 5z + 8

b. x^2 + 0.6x + 1

The answer to your question is below

Step-by-step explanation:

a)

z² - 5z + 8

Equal to zero z² - 5z + 8 = 0

Subtract 8 in both sides z² - 5z + 8 - 8 = 0 - 8

Simplify z² - 5z = - 8

Divide - 5 by 2 write the result

in both sides of the equation z² - 5z + (-5/2) ² = - 8 + (-5/2) ²

to the power of 2

Simplify z² - 5z + 25/4 = - 8 + 25/4

z² - 5z + 25/4 = - 32/4 + 25/4

z² - 5z + 25/4 = - 7/4

Factor (z - 5/2) ² = - 7/4

b)

x² - 0.6x + 1

Convert 0.6 to a fraction 0.6 = 6/10 = 3/5

x² - 3/5x + 1

Equal to zero x² - 3/5x + 1 = 0

Subtract - 1 in both sides z² - 3/5z + 1 - 1 = 0 - 1

Simplify z² - 3/5z = - 1

Divide - 3/5 by 2 write the result

in both sides of the equation z² - 3/5z + (-3/10) ² = - 1 + (-3/10) ²

to the power of 2

Simplify z² - 3/5z + 9/100 = - 1 + 9/100

z² - 3/5z + 9/100 = - 100/100 + 9/100

z² - 3/5z + 9/100 = - 91/100

Factor (z - 3/10) ² = - 91/100