Solve 2/2c^2+1/c^2=1

$$\frac { 2 } { 2 c ^ { 2 } } + \frac { 1 } { c ^ { 2 } } = 1$$

Solve for c

$$c=\sqrt{2}\approx 1.414213562$$

$$c=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2c^{2}, the least common multiple of 2c^{2},c^{2}.

$$2+2=2c^{2}$$

Add 2 and 2 to get 4.

$$4=2c^{2}$$

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

$$2c^{2}=4$$

Divide both sides by 2.

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

Divide 4 by 2 to get 2.

$$c^{2}=2$$

Take the square root of both sides of the equation.

$$c=\sqrt{2} c=-\sqrt{2}$$

Steps Using the Quadratic Formula

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2c^{2}, the least common multiple of 2c^{2},c^{2}.

$$2+2=2c^{2}$$

Add 2 and 2 to get 4.

$$4=2c^{2}$$

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

$$2c^{2}=4$$

Subtract 4 from both sides.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$c=\frac{0±\sqrt{-8\left(-4\right)}}{2\times 2}$$

Multiply -8 times -4.

$$c=\frac{0±\sqrt{32}}{2\times 2}$$

Take the square root of 32.

$$c=\frac{0±4\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$c=\frac{0±4\sqrt{2}}{4}$$

Now solve the equation c=\frac{0±4\sqrt{2}}{4} when ± is plus.

$$c=\sqrt{2}$$

Now solve the equation c=\frac{0±4\sqrt{2}}{4} when ± is minus.

$$c=-\sqrt{2}$$

The equation is now solved.

$$c=\sqrt{2} c=-\sqrt{2}$$