Algebra Examples

Solve: ${(x + 3)}^{2} - 3 = 49$

Step 1

Add $3$ to both sides of the equation.

${(x + 3)}^{2} = 49 + 3$

Step 2

Add $49$ and $3$ .

${(x + 3)}^{2} = 52$

Step 3

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

$x + 3 = \pm \sqrt{52}$

Step 4

Simplify $\pm \sqrt{52}$ .

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Step 4.1

Rewrite $52$ as $2^{2} \cdot 13$ .

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Step 4.1.1

Factor $4$ out of $52$ .

$x + 3 = \pm \sqrt{4 (13)}$

Step 4.1.2

Rewrite $4$ as $2^{2}$ .

$x + 3 = \pm \sqrt{2^{2} \cdot 13}$

Step 4.2

Pull terms out from under the radical.

$x + 3 = \pm 2 \sqrt{13}$

Step 5

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

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Step 5.1

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

$x + 3 = 2 \sqrt{13}$

Step 5.2

Subtract $3$ from both sides of the equation.

$x = 2 \sqrt{13} - 3$

Step 5.3

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

$x + 3 = - 2 \sqrt{13}$

Step 5.4

Subtract $3$ from both sides of the equation.

$x = - 2 \sqrt{13} - 3$

Step 5.5

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

$x = 2 \sqrt{13} - 3, - 2 \sqrt{13} - 3$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{13} - 3, - 2 \sqrt{13} - 3$

Decimal Form:

$x = 4.21110255 \dots, - 10.21110255 \dots$