Question

All my points to whoever can solve this

5z2−9z=−7z−5
Solve the following quadratic equation by using the quadratic formula. If needed, submit your answer as a fraction reduced to lowest terms or round your answer to two decimal places.
there are 2 different answers

Answer 1

1/5 + 2/5 i sqrt(6) = .2 + .98i

1/5 - 2/5 i sqrt(6) = .2 - .98i

Explanation:

5z^2−9z=−7z−5

We need to get all the terms on one side (set the right side equal to zero)

Add 7z to each side

5z^2−9z+7z=−7z+7z−5

5z^2−2z=−5

Add 5 to each side

5z^2−2z+5=−5 +5

5z^2−2z+5=0

This is in the form

az^2 +bz+c = 0 so we can use the quadratic formula

where a = 5 b = -2 and c = 5

-b± sqrt(b^2-4ac)

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2a

-(-2)± sqrt((-2)^2-4(5)5)

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2(5)

2± sqrt(4-100)

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10

2± sqrt(-96)

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10

2± sqrt(16)sqrt(-1) sqrt(6)

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10

2± 4i sqrt(6)

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10

1/5 ± 2/5 i sqrt(6)

Splitting the ±

1/5 + 2/5 i sqrt(6) = .2 + .98i

1/5 - 2/5 i sqrt(6) = .2 - .98i