Solve 33075=x*3x

$$33075 = x \times 3 x$$

Solve for x

$$x=105$$

$$x=-105$$

Steps by Finding Square Root

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

$$33075=x^{2}\times 3$$

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

$$x^{2}\times 3=33075$$

Divide both sides by 3.

$$x^{2}=\frac{33075}{3}$$

Divide 33075 by 3 to get 11025.

$$x^{2}=11025$$

Take the square root of both sides of the equation.

$$x=105 x=-105$$

Steps Using the Quadratic Formula

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

$$33075=x^{2}\times 3$$

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

$$x^{2}\times 3=33075$$

Subtract 33075 from both sides.

$$x^{2}\times 3-33075=0$$

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.

$$3x^{2}-33075=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -33075 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-33075\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-33075\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-33075\right)}}{2\times 3}$$

Multiply -12 times -33075.

$$x=\frac{0±\sqrt{396900}}{2\times 3}$$

Take the square root of 396900.

$$x=\frac{0±630}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±630}{6}$$

Now solve the equation x=\frac{0±630}{6} when ± is plus. Divide 630 by 6.

$$x=105$$

Now solve the equation x=\frac{0±630}{6} when ± is minus. Divide -630 by 6.

$$x=-105$$

The equation is now solved.

$$x=105 x=-105$$