Solve by Factoring 7x^2=35

$7 x^{2} = 35$

Step 1

Subtract $35$ from both sides of the equation.

$7 x^{2} - 35 = 0$

Step 2

Factor $7$ out of $7 x^{2} - 35$ .

Factor $7$ out of $7 x^{2}$ .

$7 (x^{2}) - 35 = 0$

Factor $7$ out of $- 35$ .

$7 x^{2} + 7 \cdot - 5 = 0$

Factor $7$ out of $7 x^{2} + 7 \cdot - 5$ .

$7 (x^{2} - 5) = 0$

Step 3

Divide each term in $7 (x^{2} - 5) = 0$ by $7$ and simplify.

Divide each term in $7 (x^{2} - 5) = 0$ by $7$ .

$\frac{7 (x^{2} - 5)}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (x^{2} - 5)}{7} = \frac{0}{7}$

Divide $x^{2} - 5$ by $1$ .

$x^{2} - 5 = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$x^{2} - 5 = 0$

Step 4

Add $5$ to both sides of the equation.

$x^{2} = 5$

Step 5

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

$x = \pm \sqrt{5}$

Step 6

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.

$x = \sqrt{5}$

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

$x = - \sqrt{5}$

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

$x = \sqrt{5}, - \sqrt{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$