Solve 3(x-4)^2=-6

$$3 ( x - 4 ) ^ { 2 } = - 6$$

Solve for x (complex solution)

$$x=-\sqrt{2}i+4\approx 4-1.414213562i$$

$$x=4+\sqrt{2}i\approx 4+1.414213562i$$

Steps by Finding Square Root

Dividing by 3 undoes the multiplication by 3.

$$\left(x-4\right)^{2}=-\frac{6}{3}$$

Divide -6 by 3.

$$\left(x-4\right)^{2}=-2$$

Take the square root of both sides of the equation.

$$x-4=\sqrt{2}i x-4=-\sqrt{2}i$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=\sqrt{2}i-\left(-4\right) x-4-\left(-4\right)=-\sqrt{2}i-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=\sqrt{2}i-\left(-4\right) x=-\sqrt{2}i-\left(-4\right)$$

Subtract -4 from i\sqrt{2}.

$$x=4+\sqrt{2}i$$

Subtract -4 from -i\sqrt{2}.

$$x=-\sqrt{2}i+4$$

The equation is now solved.

$$x=4+\sqrt{2}i x=-\sqrt{2}i+4$$