What are the solutions to the equation 6x-27=x^2 ?

The solutions to the equation 6x-27=x^2 are x=3+3sqrt(2)i,x=3-3sqrt(2)i

Find the zeros of 6x-27=x^2

The zeros of 6x-27=x^2 are x=3+3sqrt(2)i,x=3-3sqrt(2)i

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6 x - 27 = x^{2}

x = 3 + 32 i, x = 3 - 32 i

Solution steps

6 x - 27 = x^{2}

Switch sides

x^{2} = 6 x - 27

Move

27

to the left side

x^{2} + 27 = 6 x

Move

6 x

to the left side

x^{2} + 27 - 6 x = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - 6 x + 27 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 27}{2 \cdot 1}

Simplify

(- 6)^{2} - 4 \cdot 1 \cdot 27 : 62 i

x_{1, 2} = \frac{- ( - 6 ) \pm 6 2 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 6 2 i}{2 \cdot 1}, x_{2} = \frac{- ( - 6 ) - 6 2 i}{2 \cdot 1}

x = \frac{- ( - 6 ) + 6 2 i}{2 \cdot 1} : 3 + 32 i

x = \frac{- ( - 6 ) - 6 2 i}{2 \cdot 1} : 3 - 32 i

The solutions to the quadratic equation are:

x = 3 + 32 i, x = 3 - 32 i

- 2 x + x^{2} = 0

x^{2} - 30 = 24 - 3 x

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

3 x^{2} - 20 x + 32 = 0

- x^{2} + 2 x + 8

What are the solutions to the equation 6x-27=x^2 ?
The solutions to the equation 6x-27=x^2 are x=3+3sqrt(2)i,x=3-3sqrt(2)i
Find the zeros of 6x-27=x^2
The zeros of 6x-27=x^2 are x=3+3sqrt(2)i,x=3-3sqrt(2)i