Solve (3x-6)^2=-36x

$$( 3 x - 6 ) ^ { 2 } = - 36 x$$

Solve for x (complex solution)

$$x=2i$$

$$x=-2i$$

Steps by Finding Square Root

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-6\right)^{2}.

$$9x^{2}-36x+36=-36x$$

Add 36x to both sides.

$$9x^{2}-36x+36+36x=0$$

Combine -36x and 36x to get 0.

$$9x^{2}+36=0$$

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$9x^{2}=-36$$

Divide both sides by 9.

$$x^{2}=\frac{-36}{9}$$

Divide -36 by 9 to get -4.

$$x^{2}=-4$$

The equation is now solved.

$$x=2i x=-2i$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-6\right)^{2}.

$$9x^{2}-36x+36=-36x$$

Add 36x to both sides.

$$9x^{2}-36x+36+36x=0$$

Combine -36x and 36x to get 0.

$$9x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\times 36}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\times 36}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\times 36}}{2\times 9}$$

Multiply -36 times 36.

$$x=\frac{0±\sqrt{-1296}}{2\times 9}$$

Take the square root of -1296.

$$x=\frac{0±36i}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±36i}{18}$$

Now solve the equation x=\frac{0±36i}{18} when ± is plus.

$$x=2i$$

Now solve the equation x=\frac{0±36i}{18} when ± is minus.

$$x=-2i$$

The equation is now solved.

$$x=2i x=-2i$$