What are the solutions to the equation solvefor x,x^2+4y^2+4xy+12=0 ?

The solutions to the equation solvefor x,x^2+4y^2+4xy+12=0 are x=-2y+2sqrt(3)i,x=-2y-2sqrt(3)i

Find the zeros of solvefor x,x^2+4y^2+4xy+12=0

The zeros of solvefor x,x^2+4y^2+4xy+12=0 are x=-2y+2sqrt(3)i,x=-2y-2sqrt(3)i

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solve for

x, x^{2} + 4 y^{2} + 4 x y + 12 = 0

x = - 2 y + 23 i, x = - 2 y - 23 i

Solution steps

x^{2} + 4 y^{2} + 4 x y + 12 = 0

Write in the standard form

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

x^{2} + 4 y x + 4 y^{2} + 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 y \pm ( 4 y ) ^{2} - 4 \cdot 1 \cdot ( 4 y ^{2} + 12 )}{2 \cdot 1}

Simplify

(4 y)^{2} - 4 \cdot 1 \cdot (4 y^{2} + 12) : 43 i

x_{1, 2} = \frac{- 4 y \pm 4 3 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 4 y + 4 3 i}{2 \cdot 1}, x_{2} = \frac{- 4 y - 4 3 i}{2 \cdot 1}

x = \frac{- 4 y + 4 3 i}{2 \cdot 1} : - 2 y + 23 i

x = \frac{- 4 y - 4 3 i}{2 \cdot 1} : - 2 y - 23 i

The solutions to the quadratic equation are:

x = - 2 y + 23 i, x = - 2 y - 23 i

\frac{1}{2} x^{2} + x + 1 = 0

y^{2} - 7 = 0

6 x^{2} + 10 x + 4 = 0

5 x^{2} + 6 x - 25 = 0

x, 2 x^{2} - 8 x + 5 = 0

What are the solutions to the equation solvefor x,x^2+4y^2+4xy+12=0 ?
The solutions to the equation solvefor x,x^2+4y^2+4xy+12=0 are x=-2y+2sqrt(3)i,x=-2y-2sqrt(3)i
Find the zeros of solvefor x,x^2+4y^2+4xy+12=0
The zeros of solvefor x,x^2+4y^2+4xy+12=0 are x=-2y+2sqrt(3)i,x=-2y-2sqrt(3)i