Solve 225=b(b-16)

$$225 = b ( b - 16 )$$

Solve for b

$$b=-9$$

$$b=25$$

Steps Using the Quadratic Formula

Use the distributive property to multiply b by b-16.

$$225=b^{2}-16b$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}-16b=225$$

Subtract 225 from both sides.

$$b^{2}-16b-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -16 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-225\right)}}{2}$$

Square -16.

$$b=\frac{-\left(-16\right)±\sqrt{256-4\left(-225\right)}}{2}$$

Multiply -4 times -225.

$$b=\frac{-\left(-16\right)±\sqrt{256+900}}{2}$$

Add 256 to 900.

$$b=\frac{-\left(-16\right)±\sqrt{1156}}{2}$$

Take the square root of 1156.

$$b=\frac{-\left(-16\right)±34}{2}$$

The opposite of -16 is 16.

$$b=\frac{16±34}{2}$$

Now solve the equation b=\frac{16±34}{2} when ± is plus. Add 16 to 34.

$$b=\frac{50}{2}$$

Divide 50 by 2.

$$b=25$$

Now solve the equation b=\frac{16±34}{2} when ± is minus. Subtract 34 from 16.

$$b=-\frac{18}{2}$$

Divide -18 by 2.

$$b=-9$$

The equation is now solved.

$$b=25 b=-9$$

Steps for Completing the Square

Use the distributive property to multiply b by b-16.

$$225=b^{2}-16b$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}-16b=225$$

Divide -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$b^{2}-16b+\left(-8\right)^{2}=225+\left(-8\right)^{2}$$

Square -8.

$$b^{2}-16b+64=225+64$$

Add 225 to 64.

$$b^{2}-16b+64=289$$

Factor b^{2}-16b+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(b-8\right)^{2}=289$$

Take the square root of both sides of the equation.

$$\sqrt{\left(b-8\right)^{2}}=\sqrt{289}$$

Simplify.

$$b-8=17 b-8=-17$$

Add 8 to both sides of the equation.

$$b=25 b=-9$$