Solve Using the Square Root Property (z+4)^2=3

${(z + 4)}^{2} = 3$

Step 1

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

$z + 4 = \pm \sqrt{3}$

Step 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.

$z + 4 = \sqrt{3}$

Subtract $4$ from both sides of the equation.

$z = \sqrt{3} - 4$

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

$z + 4 = - \sqrt{3}$

Subtract $4$ from both sides of the equation.

$z = - \sqrt{3} - 4$

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

$z = \sqrt{3} - 4, - \sqrt{3} - 4$

Step 3

The result can be shown in multiple forms.

Exact Form:

$z = \sqrt{3} - 4, - \sqrt{3} - 4$

Decimal Form:

$z = - 2.26794919 \dots, - 5.73205080 \dots$