Solve w^2=13w

$$w ^ { 2 } = 13 w$$

Solve for w

$$w=13$$

$$w=0$$

Steps Using Factoring

Subtract 13w from both sides.

$$w^{2}-13w=0$$

Factor out w.

$$w\left(w-13\right)=0$$

To find equation solutions, solve w=0 and w-13=0.

$$w=0 w=13$$

Steps Using the Quadratic Formula

Subtract 13w from both sides.

$$w^{2}-13w=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -13 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}}}{2}$$

Take the square root of \left(-13\right)^{2}.

$$w=\frac{-\left(-13\right)±13}{2}$$

The opposite of -13 is 13.

$$w=\frac{13±13}{2}$$

Now solve the equation w=\frac{13±13}{2} when ± is plus. Add 13 to 13.

$$w=\frac{26}{2}$$

Divide 26 by 2.

$$w=13$$

Now solve the equation w=\frac{13±13}{2} when ± is minus. Subtract 13 from 13.

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

Divide 0 by 2.

$$w=0$$

The equation is now solved.

$$w=13 w=0$$

Steps for Completing the Square

Subtract 13w from both sides.

$$w^{2}-13w=0$$

Divide -13, the coefficient of the x term, by 2 to get -\frac{13}{2}. Then add the square of -\frac{13}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}-13w+\left(-\frac{13}{2}\right)^{2}=\left(-\frac{13}{2}\right)^{2}$$

Square -\frac{13}{2} by squaring both the numerator and the denominator of the fraction.

$$w^{2}-13w+\frac{169}{4}=\frac{169}{4}$$

Factor w^{2}-13w+\frac{169}{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}.

$$\left(w-\frac{13}{2}\right)^{2}=\frac{169}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w-\frac{13}{2}\right)^{2}}=\sqrt{\frac{169}{4}}$$

Simplify.

$$w-\frac{13}{2}=\frac{13}{2} w-\frac{13}{2}=-\frac{13}{2}$$

Add \frac{13}{2} to both sides of the equation.

$$w=13 w=0$$