Solve for c 5c^2-1=124

$5 c^{2} - 1 = 124$

Step 1

Move all terms not containing $c$ to the right side of the equation.

Add $1$ to both sides of the equation.

$5 c^{2} = 124 + 1$

Add $124$ and $1$ .

$5 c^{2} = 125$

Step 2

Divide each term in $5 c^{2} = 125$ by $5$ and simplify.

Divide each term in $5 c^{2} = 125$ by $5$ .

$\frac{5 c^{2}}{5} = \frac{125}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 c^{2}}{5} = \frac{125}{5}$

Divide $c^{2}$ by $1$ .

$c^{2} = \frac{125}{5}$

Simplify the right side.

Divide $125$ by $5$ .

$c^{2} = 25$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$c = \pm \sqrt{25}$

Step 4

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$c = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$c = \pm 5$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$c = 5$

Next, use the negative value of the $\pm$ to find the second solution.

$c = - 5$

The complete solution is the result of both the positive and negative portions of the solution.

$c = 5, - 5$