Solve 6^2=x(x*3)

$${ 6 }^{ 2 } =x(x \times 3)$$

Solve for x

$$x=2\sqrt{3}\approx 3.464101615$$

$$x=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$6^{2}=x^{2}\times 3$$

Calculate 6 to the power of 2 and get 36.

$$36=x^{2}\times 3$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 3=36$$

Divide both sides by 3.

$$x^{2}=\frac{36}{3}$$

Divide 36 by 3 to get 12.

$$x^{2}=12$$

Take the square root of both sides of the equation.

$$x=2\sqrt{3} x=-2\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$6^{2}=x^{2}\times 3$$

Calculate 6 to the power of 2 and get 36.

$$36=x^{2}\times 3$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}\times 3=36$$

Subtract 36 from both sides.

$$x^{2}\times 3-36=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-36\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-36\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-36\right)}}{2\times 3}$$

Multiply -12 times -36.

$$x=\frac{0±\sqrt{432}}{2\times 3}$$

Take the square root of 432.

$$x=\frac{0±12\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±12\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±12\sqrt{3}}{6} when ± is plus.

$$x=2\sqrt{3}$$

Now solve the equation x=\frac{0±12\sqrt{3}}{6} when ± is minus.

$$x=-2\sqrt{3}$$

The equation is now solved.

$$x=2\sqrt{3} x=-2\sqrt{3}$$