Solve x=x*7x*3

$$x=x \times 7x \times 3$$

Solve for x

$$x=\frac{1}{21}\approx 0.047619048$$

$$x=0$$

Steps Using Factoring

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

$$x=x^{2}\times 7\times 3$$

Multiply 7 and 3 to get 21.

$$x=x^{2}\times 21$$

Subtract x^{2}\times 21 from both sides.

$$x-x^{2}\times 21=0$$

Multiply -1 and 21 to get -21.

$$x-21x^{2}=0$$

Factor out x.

$$x\left(1-21x\right)=0$$

To find equation solutions, solve x=0 and 1-21x=0.

$$x=0 x=\frac{1}{21}$$

Steps Using the Quadratic Formula

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

$$x=x^{2}\times 7\times 3$$

Multiply 7 and 3 to get 21.

$$x=x^{2}\times 21$$

Subtract x^{2}\times 21 from both sides.

$$x-x^{2}\times 21=0$$

Multiply -1 and 21 to get -21.

$$x-21x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-21x^{2}+x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -21 for a, 1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}}}{2\left(-21\right)}$$

Take the square root of 1^{2}.

$$x=\frac{-1±1}{2\left(-21\right)}$$

Multiply 2 times -21.

$$x=\frac{-1±1}{-42}$$

Now solve the equation x=\frac{-1±1}{-42} when ± is plus. Add -1 to 1.

$$x=\frac{0}{-42}$$

Divide 0 by -42.

$$x=0$$

Now solve the equation x=\frac{-1±1}{-42} when ± is minus. Subtract 1 from -1.

$$x=-\frac{2}{-42}$$

Reduce the fraction \frac{-2}{-42} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{21}$$

The equation is now solved.

$$x=0 x=\frac{1}{21}$$

Steps for Completing the Square

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

$$x=x^{2}\times 7\times 3$$

Multiply 7 and 3 to get 21.

$$x=x^{2}\times 21$$

Subtract x^{2}\times 21 from both sides.

$$x-x^{2}\times 21=0$$

Multiply -1 and 21 to get -21.

$$x-21x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-21x^{2}+x=0$$

Divide both sides by -21.

$$\frac{-21x^{2}+x}{-21}=\frac{0}{-21}$$

Dividing by -21 undoes the multiplication by -21.

$$x^{2}+\frac{1}{-21}x=\frac{0}{-21}$$

Divide 1 by -21.

$$x^{2}-\frac{1}{21}x=\frac{0}{-21}$$

Divide 0 by -21.

$$x^{2}-\frac{1}{21}x=0$$

Divide -\frac{1}{21}, the coefficient of the x term, by 2 to get -\frac{1}{42}. Then add the square of -\frac{1}{42} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1}{21}x+\left(-\frac{1}{42}\right)^{2}=\left(-\frac{1}{42}\right)^{2}$$

Square -\frac{1}{42} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1}{21}x+\frac{1}{1764}=\frac{1}{1764}$$

Factor x^{2}-\frac{1}{21}x+\frac{1}{1764}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{42}\right)^{2}=\frac{1}{1764}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{42}\right)^{2}}=\sqrt{\frac{1}{1764}}$$

Simplify.

$$x-\frac{1}{42}=\frac{1}{42} x-\frac{1}{42}=-\frac{1}{42}$$

Add \frac{1}{42} to both sides of the equation.

$$x=\frac{1}{21} x=0$$