Algebra Examples

$5 {(x - 10)}^{2} - 33 = - 3$

Step 1

Add $33$ to both sides of the equation.

$5 {(x - 10)}^{2} = - 3 + 33$

Step 2

Add $- 3$ and $33$ .

$5 {(x - 10)}^{2} = 30$

Step 3

Divide each term in $5 {(x - 10)}^{2} = 30$ by $5$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $5 {(x - 10)}^{2} = 30$ by $5$ .

$\frac{5 {(x - 10)}^{2}}{5} = \frac{30}{5}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{5 {(x - 10)}^{2}}{5} = \frac{30}{5}$

Step 3.2.1.2

Divide ${(x - 10)}^{2}$ by $1$ .

${(x - 10)}^{2} = \frac{30}{5}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $30$ by $5$ .

${(x - 10)}^{2} = 6$

Step 4

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

$x - 10 = \pm \sqrt{6}$

Step 5

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

Tap for more steps...

Step 5.1

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

$x - 10 = \sqrt{6}$

Step 5.2

Add $10$ to both sides of the equation.

$x = \sqrt{6} + 10$

Step 5.3

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

$x - 10 = - \sqrt{6}$

Step 5.4

Add $10$ to both sides of the equation.

$x = - \sqrt{6} + 10$

Step 5.5

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

$x = \sqrt{6} + 10, - \sqrt{6} + 10$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{6} + 10, - \sqrt{6} + 10$

Decimal Form:

$x = 12.44948974 \dots, 7.55051025 \dots$