Solve for x 4(x^2-5)-1=3

$4 (x^{2} - 5) - 1 = 3$

Simplify $4 (x^{2} - 5) - 1$ .

Simplify each term.

Apply the distributive property.

$4 x^{2} + 4 \cdot - 5 - 1 = 3$

Multiply $4$ by $- 5$ .

$4 x^{2} - 20 - 1 = 3$

Subtract $1$ from $- 20$ .

$4 x^{2} - 21 = 3$

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

Add $21$ to both sides of the equation.

$4 x^{2} = 3 + 21$

Add $3$ and $21$ .

$4 x^{2} = 24$

Divide each term in $4 x^{2} = 24$ by $4$ and simplify.

Divide each term in $4 x^{2} = 24$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{24}{4}$

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

$x^{2} = \frac{24}{4}$

Simplify the right side.

Divide $24$ by $4$ .

$x^{2} = 6$

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

$x = \pm \sqrt{6}$

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.

$x = \sqrt{6}$

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

$x = - \sqrt{6}$

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

$x = \sqrt{6}, - \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{6}, - \sqrt{6}$

Decimal Form:

$x = 2.44948974 \dots, - 2.44948974 \dots$