What are the solutions to the equation x^2=6x-11 ?

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

Find the zeros of x^2=6x-11

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

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x^{2} = 6 x - 11

x = 3 + 2 i, x = 3 - 2 i

Solution steps

x^{2} = 6 x - 11

Move

11

to the left side

x^{2} + 11 = 6 x

Move

6 x

to the left side

x^{2} + 11 - 6 x = 0

Write in the standard form

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

x^{2} - 6 x + 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 11}{2 \cdot 1}

Simplify

(- 6)^{2} - 4 \cdot 1 \cdot 11 : 22 i

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 3 + 2 i, x = 3 - 2 i

4 x^{2} + 24 x - 12 = 0

x, x^{2} + x y + y^{3} = 1

(x - 3)^{2} + 27 = 0

3 x^{2} - 42 x = - 87

x, x^{2} + x y + y^{2} = 0

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