Solve Using the Square Root Property (x-3)^2=5

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Algebra

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

Take the square root of each side of the equation to set up the solution for $x$

${(x - 3)}^{2 \cdot \frac{1}{2}} = \pm \sqrt{5}$

Remove the perfect root factor $x - 3$ under the radical to solve for $x$ .

$x - 3 = \pm \sqrt{5}$

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.

$x - 3 = \sqrt{5}$

Add $3$ to both sides of the equation.

$x = \sqrt{5} + 3$

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

$x - 3 = - \sqrt{5}$

Add $3$ to both sides of the equation.

$x = - \sqrt{5} + 3$

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

$x = \sqrt{5} + 3, - \sqrt{5} + 3$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5} + 3, - \sqrt{5} + 3$

Decimal Form:

$x = 5.23606797 \dots, 0.76393202 \dots$

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