What are the solutions to the equation x^2+23x+111=11x ?

The solutions to the equation x^2+23x+111=11x are x=-6+5sqrt(3)i,x=-6-5sqrt(3)i

Find the zeros of x^2+23x+111=11x

The zeros of x^2+23x+111=11x are x=-6+5sqrt(3)i,x=-6-5sqrt(3)i

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x^{2} + 23 x + 111 = 11 x

x = - 6 + 53 i, x = - 6 - 53 i

Solution steps

x^{2} + 23 x + 111 = 11 x

Move

11 x

to the left side

x^{2} + 12 x + 111 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 1 \cdot 111}{2 \cdot 1}

Simplify

1 2^{2} - 4 \cdot 1 \cdot 111 : 103 i

x_{1, 2} = \frac{- 12 \pm 10 3 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 12 + 10 3 i}{2 \cdot 1}, x_{2} = \frac{- 12 - 10 3 i}{2 \cdot 1}

x = \frac{- 12 + 10 3 i}{2 \cdot 1} : - 6 + 53 i

x = \frac{- 12 - 10 3 i}{2 \cdot 1} : - 6 - 53 i

The solutions to the quadratic equation are:

x = - 6 + 53 i, x = - 6 - 53 i

3^{3^{3}}

(2 x - 10) (x + 6) = 0

- 2 (1 + 3 b) > 1 - 6 b

(\frac{64}{27})^{\frac{2}{3}}

3 (2 x - 3) \geq 2 (x + 5) - 1

What are the solutions to the equation x^2+23x+111=11x ?
The solutions to the equation x^2+23x+111=11x are x=-6+5sqrt(3)i,x=-6-5sqrt(3)i
Find the zeros of x^2+23x+111=11x
The zeros of x^2+23x+111=11x are x=-6+5sqrt(3)i,x=-6-5sqrt(3)i