Solve for u 2u^2-96=0

$2 u^{2} - 96 = 0$

Step 1

Add $96$ to both sides of the equation.

$2 u^{2} = 96$

Step 2

Divide each term in $2 u^{2} = 96$ by $2$ and simplify.

Divide each term in $2 u^{2} = 96$ by $2$ .

$\frac{2 u^{2}}{2} = \frac{96}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 u^{2}}{2} = \frac{96}{2}$

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

$u^{2} = \frac{96}{2}$

Simplify the right side.

Divide $96$ by $2$ .

$u^{2} = 48$

Step 3

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

$u = \pm \sqrt{48}$

Step 4

Simplify $\pm \sqrt{48}$ .

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$u = \pm \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$u = \pm \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$u = \pm 4 \sqrt{3}$

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.

$u = 4 \sqrt{3}$

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

$u = - 4 \sqrt{3}$

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

$u = 4 \sqrt{3}, - 4 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$u = 4 \sqrt{3}, - 4 \sqrt{3}$

Decimal Form:

$u = 6.92820323 \dots, - 6.92820323 \dots$