What are the solutions to the equation n^2=-89+18n ?

The solutions to the equation n^2=-89+18n are n=9+2sqrt(2)i,n=9-2sqrt(2)i

Find the zeros of n^2=-89+18n

The zeros of n^2=-89+18n are n=9+2sqrt(2)i,n=9-2sqrt(2)i

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n^{2} = - 89 + 18 n

n = 9 + 22 i, n = 9 - 22 i

Solution steps

n^{2} = - 89 + 18 n

Move

18 n

to the left side

n^{2} - 18 n = - 89

Move

89

to the left side

n^{2} - 18 n + 89 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 1 \cdot 89}{2 \cdot 1}

Simplify

(- 18)^{2} - 4 \cdot 1 \cdot 89 : 42 i

n_{1, 2} = \frac{- ( - 18 ) \pm 4 2 i}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- ( - 18 ) + 4 2 i}{2 \cdot 1}, n_{2} = \frac{- ( - 18 ) - 4 2 i}{2 \cdot 1}

n = \frac{- ( - 18 ) + 4 2 i}{2 \cdot 1} : 9 + 22 i

n = \frac{- ( - 18 ) - 4 2 i}{2 \cdot 1} : 9 - 22 i

The solutions to the quadratic equation are:

n = 9 + 22 i, n = 9 - 22 i

- 3 x + 2 x + \frac{8}{4} = - x^{2}

(x + 5)^{2} - 200 = 25

t^{2} = 4 t - 4

x^{2} - x - 3 = 0

3 x^{2} - 18 = 2 x + 1

What are the solutions to the equation n^2=-89+18n ?
The solutions to the equation n^2=-89+18n are n=9+2sqrt(2)i,n=9-2sqrt(2)i
Find the zeros of n^2=-89+18n
The zeros of n^2=-89+18n are n=9+2sqrt(2)i,n=9-2sqrt(2)i