Solve x*2x=450

$$x \times 2x=450$$

Solve for x

$$x=15$$

$$x=-15$$

Steps by Finding Square Root

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

$$x^{2}\times 2=450$$

Divide both sides by 2.

$$x^{2}=\frac{450}{2}$$

Divide 450 by 2 to get 225.

$$x^{2}=225$$

Take the square root of both sides of the equation.

$$x=15 x=-15$$

Steps Using the Quadratic Formula

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

$$x^{2}\times 2=450$$

Subtract 450 from both sides.

$$x^{2}\times 2-450=0$$

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.

$$2x^{2}-450=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -450 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-450\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-450\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-450\right)}}{2\times 2}$$

Multiply -8 times -450.

$$x=\frac{0±\sqrt{3600}}{2\times 2}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±60}{4}$$

Now solve the equation x=\frac{0±60}{4} when ± is plus. Divide 60 by 4.

$$x=15$$

Now solve the equation x=\frac{0±60}{4} when ± is minus. Divide -60 by 4.

$$x=-15$$

The equation is now solved.

$$x=15 x=-15$$