Solve for x 4=x^2-7

$4 = x^{2} - 7$

Rewrite the equation as $x^{2} - 7 = 4$ .

$x^{2} - 7 = 4$

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

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Add $7$ to both sides of the equation.

$x^{2} = 4 + 7$

Add $4$ and $7$ .

$x^{2} = 11$

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

$x = \pm \sqrt{11}$

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

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First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{11}$

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

$x = - \sqrt{11}$

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

$x = \sqrt{11}, - \sqrt{11}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{11}, - \sqrt{11}$

Decimal Form:

$x = 3.31662479 \dots, - 3.31662479 \dots$