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Rewrite each expression by completing the square.
a. z^2 − 5z + 8
b. x^2 + 0.6x + 1

1 Answer

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Answer:

The answer to your question is below

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

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