Solve 3x^2-24x*50=0

$$3 { x }^{ 2 } -24x \times 50 = 0$$

Solve for x

$$x=400$$

$$x=0$$

Steps Using Factoring

Multiply 24 and 50 to get 1200.

$$3x^{2}-1200x=0$$

Factor out x.

$$x\left(3x-1200\right)=0$$

To find equation solutions, solve x=0 and 3x-1200=0.

$$x=0 x=400$$

Steps Using the Quadratic Formula

Multiply 24 and 50 to get 1200.

$$3x^{2}-1200x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, -1200 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1200\right)±\sqrt{\left(-1200\right)^{2}}}{2\times 3}$$

Take the square root of \left(-1200\right)^{2}.

$$x=\frac{-\left(-1200\right)±1200}{2\times 3}$$

The opposite of -1200 is 1200.

$$x=\frac{1200±1200}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{1200±1200}{6}$$

Now solve the equation x=\frac{1200±1200}{6} when ± is plus. Add 1200 to 1200.

$$x=\frac{2400}{6}$$

Divide 2400 by 6.

$$x=400$$

Now solve the equation x=\frac{1200±1200}{6} when ± is minus. Subtract 1200 from 1200.

$$x=\frac{0}{6}$$

Divide 0 by 6.

$$x=0$$

The equation is now solved.

$$x=400 x=0$$

Steps for Completing the Square

Multiply 24 and 50 to get 1200.

$$3x^{2}-1200x=0$$

Divide both sides by 3.

$$\frac{3x^{2}-1200x}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\left(-\frac{1200}{3}\right)x=\frac{0}{3}$$

Divide -1200 by 3.

$$x^{2}-400x=\frac{0}{3}$$

Divide 0 by 3.

$$x^{2}-400x=0$$

Divide -400, the coefficient of the x term, by 2 to get -200. Then add the square of -200 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-400x+\left(-200\right)^{2}=\left(-200\right)^{2}$$

Square -200.

$$x^{2}-400x+40000=40000$$

Factor x^{2}-400x+40000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-200\right)^{2}=40000$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-200\right)^{2}}=\sqrt{40000}$$

Simplify.

$$x-200=200 x-200=-200$$

Add 200 to both sides of the equation.

$$x=400 x=0$$