What are the solutions to the equation u^2-3u=-54 ?

The solutions to the equation u^2-3u=-54 are u= 3/2+i(3sqrt(23))/2 ,u= 3/2-i(3sqrt(23))/2

Find the zeros of u^2-3u=-54

The zeros of u^2-3u=-54 are u= 3/2+i(3sqrt(23))/2 ,u= 3/2-i(3sqrt(23))/2

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u^{2} - 3 u = - 54

u = \frac{3}{2} + i \frac{3 23}{2}, u = \frac{3}{2} - i \frac{3 23}{2}

Solution steps

u^{2} - 3 u = - 54

Move

54

to the left side

u^{2} - 3 u + 54 = 0

Solve with the quadratic formula

u_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot 54}{2 \cdot 1}

Simplify

(- 3)^{2} - 4 \cdot 1 \cdot 54 : 323 i

u_{1, 2} = \frac{- ( - 3 ) \pm 3 23 i}{2 \cdot 1}

Separate the solutions

u_{1} = \frac{- ( - 3 ) + 3 23 i}{2 \cdot 1}, u_{2} = \frac{- ( - 3 ) - 3 23 i}{2 \cdot 1}

u = \frac{- ( - 3 ) + 3 23 i}{2 \cdot 1} : \frac{3}{2} + i \frac{3 23}{2}

u = \frac{- ( - 3 ) - 3 23 i}{2 \cdot 1} : \frac{3}{2} - i \frac{3 23}{2}

The solutions to the quadratic equation are:

u = \frac{3}{2} + i \frac{3 23}{2}, u = \frac{3}{2} - i \frac{3 23}{2}

6 = 7 x - 2 x^{2}

a^{2} = 6 a - 9

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

2 (3 x + 4)^{2} - 5 (3 x + 4) + 3 = 0

0 = 3 x^{2} + 4 x + 2

What are the solutions to the equation u^2-3u=-54 ?
The solutions to the equation u^2-3u=-54 are u= 3/2+i(3sqrt(23))/2 ,u= 3/2-i(3sqrt(23))/2
Find the zeros of u^2-3u=-54
The zeros of u^2-3u=-54 are u= 3/2+i(3sqrt(23))/2 ,u= 3/2-i(3sqrt(23))/2