Solve w^2=10w

$$w ^ { 2 } = 10 w$$

Solve for w

$$w=10$$

$$w=0$$

Steps Using Factoring

Subtract 10w from both sides.

$$w^{2}-10w=0$$

Factor out w.

$$w\left(w-10\right)=0$$

To find equation solutions, solve w=0 and w-10=0.

$$w=0 w=10$$

Steps Using the Quadratic Formula

Subtract 10w from both sides.

$$w^{2}-10w=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -10 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2}$$

Take the square root of \left(-10\right)^{2}.

$$w=\frac{-\left(-10\right)±10}{2}$$

The opposite of -10 is 10.

$$w=\frac{10±10}{2}$$

Now solve the equation w=\frac{10±10}{2} when ± is plus. Add 10 to 10.

$$w=\frac{20}{2}$$

Divide 20 by 2.

$$w=10$$

Now solve the equation w=\frac{10±10}{2} when ± is minus. Subtract 10 from 10.

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

Divide 0 by 2.

$$w=0$$

The equation is now solved.

$$w=10 w=0$$

Steps for Completing the Square

Subtract 10w from both sides.

$$w^{2}-10w=0$$

Divide -10, the coefficient of the x term, by 2 to get -5. Then add the square of -5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$w^{2}-10w+\left(-5\right)^{2}=\left(-5\right)^{2}$$

Square -5.

$$w^{2}-10w+25=25$$

Factor w^{2}-10w+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(w-5\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(w-5\right)^{2}}=\sqrt{25}$$

Simplify.

$$w-5=5 w-5=-5$$

Add 5 to both sides of the equation.

$$w=10 w=0$$