Algebra Examples

$4 {(x - 6)}^{2} - 27 = - 23$

Step 1

Add $27$ to both sides of the equation.

$4 {(x - 6)}^{2} = - 23 + 27$

Step 2

Add $- 23$ and $27$ .

$4 {(x - 6)}^{2} = 4$

Step 3

Divide each term in $4 {(x - 6)}^{2} = 4$ by $4$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $4 {(x - 6)}^{2} = 4$ by $4$ .

$\frac{4 {(x - 6)}^{2}}{4} = \frac{4}{4}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{4 {(x - 6)}^{2}}{4} = \frac{4}{4}$

Step 3.2.1.2

Divide ${(x - 6)}^{2}$ by $1$ .

${(x - 6)}^{2} = \frac{4}{4}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $4$ by $4$ .

${(x - 6)}^{2} = 1$

Step 4

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

$x - 6 = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$x - 6 = \pm 1$

Step 6

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

Tap for more steps...

Step 6.1

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

$x - 6 = 1$

Step 6.2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 6.2.1

Add $6$ to both sides of the equation.

$x = 1 + 6$

Step 6.2.2

Add $1$ and $6$ .

$x = 7$

Step 6.3

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

$x - 6 = - 1$

Step 6.4

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 6.4.1

Add $6$ to both sides of the equation.

$x = - 1 + 6$

Step 6.4.2

Add $- 1$ and $6$ .

$x = 5$

Step 6.5

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

$x = 7, 5$