Solve j^2=j

$$j ^ { 2 } = j$$

Solve for j

$$j=1$$

$$j=0$$

Steps Using Factoring

Subtract j from both sides.

$$j^{2}-j=0$$

Factor out j.

$$j\left(j-1\right)=0$$

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

$$j=0 j=1$$

Steps Using the Quadratic Formula

Subtract j from both sides.

$$j^{2}-j=0$$

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

$$j=\frac{-\left(-1\right)±\sqrt{1}}{2}$$

Take the square root of 1.

$$j=\frac{-\left(-1\right)±1}{2}$$

The opposite of -1 is 1.

$$j=\frac{1±1}{2}$$

Now solve the equation j=\frac{1±1}{2} when ± is plus. Add 1 to 1.

$$j=\frac{2}{2}$$

Divide 2 by 2.

$$j=1$$

Now solve the equation j=\frac{1±1}{2} when ± is minus. Subtract 1 from 1.

$$j=\frac{0}{2}$$

Divide 0 by 2.

$$j=0$$

The equation is now solved.

$$j=1 j=0$$

Steps for Completing the Square

Subtract j from both sides.

$$j^{2}-j=0$$

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

$$j^{2}-j+\left(-\frac{1}{2}\right)^{2}=\left(-\frac{1}{2}\right)^{2}$$

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$j^{2}-j+\frac{1}{4}=\frac{1}{4}$$

Factor j^{2}-j+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(j-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(j-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Simplify.

$$j-\frac{1}{2}=\frac{1}{2} j-\frac{1}{2}=-\frac{1}{2}$$

Add \frac{1}{2} to both sides of the equation.

$$j=1 j=0$$