Solve for x 7x^2+1=8

$7 x^{2} + 1 = 8$

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

Subtract $1$ from both sides of the equation.

$7 x^{2} = 8 - 1$

Subtract $1$ from $8$ .

$7 x^{2} = 7$

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

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

$\frac{7 x^{2}}{7} = \frac{7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{7}{7}$

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

$x^{2} = \frac{7}{7}$

Simplify the right side.

Divide $7$ by $7$ .

$x^{2} = 1$

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

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

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.

$x = 1$

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

$x = - 1$

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

$x = 1, - 1$