Solve x*2x=400000

$$x \times 2x = 400000$$

Solve for x

$$x=200\sqrt{5}\approx 447.2135955$$

$$x=-200\sqrt{5}\approx -447.2135955$$

Steps by Finding Square Root

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

$$x^{2}\times 2=400000$$

Divide both sides by 2.

$$x^{2}=\frac{400000}{2}$$

Divide 400000 by 2 to get 200000.

$$x^{2}=200000$$

Take the square root of both sides of the equation.

$$x=200\sqrt{5} x=-200\sqrt{5}$$

Steps Using the Quadratic Formula

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

$$x^{2}\times 2=400000$$

Subtract 400000 from both sides.

$$x^{2}\times 2-400000=0$$

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.

$$2x^{2}-400000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -400000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-400000\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-400000\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-400000\right)}}{2\times 2}$$

Multiply -8 times -400000.

$$x=\frac{0±\sqrt{3200000}}{2\times 2}$$

Take the square root of 3200000.

$$x=\frac{0±800\sqrt{5}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±800\sqrt{5}}{4}$$

Now solve the equation x=\frac{0±800\sqrt{5}}{4} when ± is plus.

$$x=200\sqrt{5}$$

Now solve the equation x=\frac{0±800\sqrt{5}}{4} when ± is minus.

$$x=-200\sqrt{5}$$

The equation is now solved.

$$x=200\sqrt{5} x=-200\sqrt{5}$$