Solve for a a=49/a

$a = \frac{49}{a}$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, a$

The LCM of one and any expression is the expression.

$a$

Multiply each term in $a = \frac{49}{a}$ by $a$ to eliminate the fractions.

Multiply each term in $a = \frac{49}{a}$ by $a$ .

$a \cdot a = \frac{49}{a} a$

Simplify the left side.

Multiply $a$ by $a$ .

$a^{2} = \frac{49}{a} a$

Simplify the right side.

Cancel the common factor of $a$ .

Cancel the common factor.

$a^{2} = \frac{49}{a} a$

Rewrite the expression.

$a^{2} = 49$

Solve the equation.

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

$a = \pm \sqrt{49}$

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$a = \pm \sqrt{7^{2}}$

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

$a = \pm 7$

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.

$a = 7$

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

$a = - 7$

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

$a = 7, - 7$