Solve frac{10+sqrt{-6}}{2}-x=sqrt{-6}

$$\frac { 10 + \sqrt { - 6 } } { 2 } - x = \sqrt { - 6 }$$

Solve for x

$$x=-\frac{\sqrt{6}i}{2}+5\approx 5-1.224744871i$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$10+\sqrt{-6}-2x=2\sqrt{-6}$$

Factor -6=6\left(-1\right). Rewrite the square root of the product \sqrt{6\left(-1\right)} as the product of square roots \sqrt{6}\sqrt{-1}. By definition, the square root of -1 is i.

$$10+\sqrt{6}i-2x=2\sqrt{-6}$$

Factor -6=6\left(-1\right). Rewrite the square root of the product \sqrt{6\left(-1\right)} as the product of square roots \sqrt{6}\sqrt{-1}. By definition, the square root of -1 is i.

$$10+\sqrt{6}i-2x=2\sqrt{6}i$$

Multiply 2 and i to get 2i.

$$10+\sqrt{6}i-2x=2i\sqrt{6}$$

Subtract 10 from both sides.

$$\sqrt{6}i-2x=2i\sqrt{6}-10$$

Subtract \sqrt{6}i from both sides.

$$-2x=2i\sqrt{6}-10-\sqrt{6}i$$

Combine 2i\sqrt{6} and -\sqrt{6}i to get i\sqrt{6}.

$$-2x=i\sqrt{6}-10$$

The equation is in standard form.

$$-2x=-10+\sqrt{6}i$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{-10+\sqrt{6}i}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{-10+\sqrt{6}i}{-2}$$

Divide i\sqrt{6}-10 by -2.

$$x=-\frac{\sqrt{6}i}{2}+5$$