Solve 5x*6x=x

$$5 x \cdot 6 x = x$$

Solve for x

$$x=\frac{1}{30}\approx 0.033333333$$

$$x=0$$

Steps Using Factoring

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

$$5x^{2}\times 6=x$$

Multiply 5 and 6 to get 30.

$$30x^{2}=x$$

Subtract x from both sides.

$$30x^{2}-x=0$$

Factor out x.

$$x\left(30x-1\right)=0$$

To find equation solutions, solve x=0 and 30x-1=0.

$$x=0 x=\frac{1}{30}$$

Steps Using the Quadratic Formula

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

$$5x^{2}\times 6=x$$

Multiply 5 and 6 to get 30.

$$30x^{2}=x$$

Subtract x from both sides.

$$30x^{2}-x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 30 for a, -1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 30}$$

Take the square root of 1.

$$x=\frac{-\left(-1\right)±1}{2\times 30}$$

The opposite of -1 is 1.

$$x=\frac{1±1}{2\times 30}$$

Multiply 2 times 30.

$$x=\frac{1±1}{60}$$

Now solve the equation x=\frac{1±1}{60} when ± is plus. Add 1 to 1.

$$x=\frac{2}{60}$$

Reduce the fraction \frac{2}{60} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{30}$$

Now solve the equation x=\frac{1±1}{60} when ± is minus. Subtract 1 from 1.

$$x=\frac{0}{60}$$

Divide 0 by 60.

$$x=0$$

The equation is now solved.

$$x=\frac{1}{30} x=0$$

Steps for Completing the Square

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

$$5x^{2}\times 6=x$$

Multiply 5 and 6 to get 30.

$$30x^{2}=x$$

Subtract x from both sides.

$$30x^{2}-x=0$$

Divide both sides by 30.

$$\frac{30x^{2}-x}{30}=\frac{0}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$x^{2}-\frac{1}{30}x=\frac{0}{30}$$

Divide 0 by 30.

$$x^{2}-\frac{1}{30}x=0$$

Divide -\frac{1}{30}, the coefficient of the x term, by 2 to get -\frac{1}{60}. Then add the square of -\frac{1}{60} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1}{30}x+\left(-\frac{1}{60}\right)^{2}=\left(-\frac{1}{60}\right)^{2}$$

Square -\frac{1}{60} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1}{30}x+\frac{1}{3600}=\frac{1}{3600}$$

Factor x^{2}-\frac{1}{30}x+\frac{1}{3600}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{60}\right)^{2}=\frac{1}{3600}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{60}\right)^{2}}=\sqrt{\frac{1}{3600}}$$

Simplify.

$$x-\frac{1}{60}=\frac{1}{60} x-\frac{1}{60}=-\frac{1}{60}$$

Add \frac{1}{60} to both sides of the equation.

$$x=\frac{1}{30} x=0$$