Solve 111=z^2+11

$$111 = z ^ { 2 } + 11$$

Solve for z

$$z=10$$

$$z=-10$$

Steps Using Difference of Squares

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

$$z^{2}+11=111$$

Subtract 111 from both sides.

$$z^{2}+11-111=0$$

Subtract 111 from 11 to get -100.

$$z^{2}-100=0$$

Consider z^{2}-100. Rewrite z^{2}-100 as z^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-10\right)\left(z+10\right)=0$$

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

$$z=10 z=-10$$

Steps by Finding Square Root

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

$$z^{2}+11=111$$

Subtract 11 from both sides.

$$z^{2}=111-11$$

Subtract 11 from 111 to get 100.

$$z^{2}=100$$

Take the square root of both sides of the equation.

$$z=10 z=-10$$

Steps Using the Quadratic Formula

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

$$z^{2}+11=111$$

Subtract 111 from both sides.

$$z^{2}+11-111=0$$

Subtract 111 from 11 to get -100.

$$z^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-100\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-100\right)}}{2}$$

Multiply -4 times -100.

$$z=\frac{0±\sqrt{400}}{2}$$

Take the square root of 400.

$$z=\frac{0±20}{2}$$

Now solve the equation z=\frac{0±20}{2} when ± is plus. Divide 20 by 2.

$$z=10$$

Now solve the equation z=\frac{0±20}{2} when ± is minus. Divide -20 by 2.

$$z=-10$$

The equation is now solved.

$$z=10 z=-10$$