Solve for u 7u^2-56=0

$7 u^{2} - 56 = 0$

Add $56$ to both sides of the equation.

$7 u^{2} = 56$

Divide each term in $7 u^{2} = 56$ by $7$ and simplify.

Divide each term in $7 u^{2} = 56$ by $7$ .

$\frac{7 u^{2}}{7} = \frac{56}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 u^{2}}{7} = \frac{56}{7}$

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

$u^{2} = \frac{56}{7}$

Simplify the right side.

Divide $56$ by $7$ .

$u^{2} = 8$

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

$u = \pm \sqrt{8}$

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$u = \pm \sqrt{4 (2)}$

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

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

Pull terms out from under the radical.

$u = \pm 2 \sqrt{2}$

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.

$u = 2 \sqrt{2}$

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

$u = - 2 \sqrt{2}$

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

$u = 2 \sqrt{2}, - 2 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$u = 2 \sqrt{2}, - 2 \sqrt{2}$

Decimal Form:

$u = 2.82842712 \dots, - 2.82842712 \dots$