Solve (2-2)^2/4+y^2=1

$$\frac { ( 2 - 2 ) ^ { 2 } } { 4 } + y ^ { 2 } = 1$$

Solve for y

$$y=1$$

$$y=-1$$

Steps Using Difference of Squares

Multiply both sides of the equation by 4.

$$\left(2-2\right)^{2}+4y^{2}=4$$

Subtract 2 from 2 to get 0.

$$0^{2}+4y^{2}=4$$

Calculate 0 to the power of 2 and get 0.

$$0+4y^{2}=4$$

Anything plus zero gives itself.

$$4y^{2}=4$$

Subtract 4 from both sides.

$$4y^{2}-4=0$$

Divide both sides by 4.

$$y^{2}-1=0$$

Consider y^{2}-1. Rewrite y^{2}-1 as y^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-1\right)\left(y+1\right)=0$$

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

$$y=1 y=-1$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$\left(2-2\right)^{2}+4y^{2}=4$$

Subtract 2 from 2 to get 0.

$$0^{2}+4y^{2}=4$$

Calculate 0 to the power of 2 and get 0.

$$0+4y^{2}=4$$

Anything plus zero gives itself.

$$4y^{2}=4$$

Divide both sides by 4.

$$y^{2}=\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$y^{2}=1$$

Take the square root of both sides of the equation.

$$y=1 y=-1$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$\left(2-2\right)^{2}+4y^{2}=4$$

Subtract 2 from 2 to get 0.

$$0^{2}+4y^{2}=4$$

Calculate 0 to the power of 2 and get 0.

$$0+4y^{2}=4$$

Anything plus zero gives itself.

$$4y^{2}=4$$

Subtract 4 from both sides.

$$4y^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$y=\frac{0±\sqrt{-16\left(-4\right)}}{2\times 4}$$

Multiply -16 times -4.

$$y=\frac{0±\sqrt{64}}{2\times 4}$$

Take the square root of 64.

$$y=\frac{0±8}{2\times 4}$$

Multiply 2 times 4.

$$y=\frac{0±8}{8}$$

Now solve the equation y=\frac{0±8}{8} when ± is plus. Divide 8 by 8.

$$y=1$$

Now solve the equation y=\frac{0±8}{8} when ± is minus. Divide -8 by 8.

$$y=-1$$

The equation is now solved.

$$y=1 y=-1$$