Question

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Answer 1

The equation after completing the square is (z + 4)² = 80

The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5

Completing the square

From the question, we are to solve the given quadratic equation by completing the square

The given equation is

z² +8z - 44 =20

First, add 44 to both sides of the equation

z² +8z - 44 + 44 = 20 + 44

z² +8z = 64

Now, divide the coefficient of z by 2, square the value and add to both sides

The coefficient of z is 8

Dividing

8/2 = 4

Squaring

4²

Now, add this to both sides

That is,

z² +8z +4² = 64 + 4²

(z + 4)² = 64 + 16

(z + 4)² = 80

The equation after completing the square is  

(z + 4)² = 80

Continuation

(z + 4)² = 80

Take the square root of both sides

√(z + 4)² = ±√80

z + 4 = ±√80

z = -4 ± √80

z = -4 ± 4√5

z = -4 + 4√5 and z = -4 - 4√5

Hence,

The equation after completing the square is (z + 4)² = 80

The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5

Learn more on Completing the square here: brainly.com/question/49444

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