Find the Roots (Zeros) (x+3)^2-3=0

${(x + 3)}^{2} - 3 = 0$

Step 1

Add $3$ to both sides of the equation.

${(x + 3)}^{2} = 3$

Step 2

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

$x + 3 = \pm \sqrt{3}$

Step 3

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.

$x + 3 = \sqrt{3}$

Subtract $3$ from both sides of the equation.

$x = \sqrt{3} - 3$

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

$x + 3 = - \sqrt{3}$

Subtract $3$ from both sides of the equation.

$x = - \sqrt{3} - 3$

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

$x = \sqrt{3} - 3, - \sqrt{3} - 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3} - 3, - \sqrt{3} - 3$

Decimal Form:

$x = - 1.26794919 \dots, - 4.73205080 \dots$

Step 5