Solve Using the Square Root Property 9(4-x)^2=27

$9 {(4 - x)}^{2} = 27$

Step 1

Divide each term in $9 {(4 - x)}^{2} = 27$ by $9$ and simplify.

Divide each term in $9 {(4 - x)}^{2} = 27$ by $9$ .

$\frac{9 {(4 - x)}^{2}}{9} = \frac{27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 {(4 - x)}^{2}}{9} = \frac{27}{9}$

Divide ${(4 - x)}^{2}$ by $1$ .

${(4 - x)}^{2} = \frac{27}{9}$

Simplify the right side.

Divide $27$ by $9$ .

${(4 - x)}^{2} = 3$

Step 2

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

$4 - x = \pm \sqrt{3}$

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.

$4 - x = \sqrt{3}$

Subtract $4$ from both sides of the equation.

$- x = \sqrt{3} - 4$

Divide each term in $- x = \sqrt{3} - 4$ by $- 1$ and simplify.

Divide each term in $- x = \sqrt{3} - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\sqrt{3}}{- 1} + \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\sqrt{3}}{- 1} + \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{3}}{- 1} + \frac{- 4}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\sqrt{3}}{- 1}$ .

$x = - 1 \cdot \sqrt{3} + \frac{- 4}{- 1}$

Rewrite $- 1 \cdot \sqrt{3}$ as $- \sqrt{3}$ .

$x = - \sqrt{3} + \frac{- 4}{- 1}$

Divide $- 4$ by $- 1$ .

$x = - \sqrt{3} + 4$

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

$4 - x = - \sqrt{3}$

Subtract $4$ from both sides of the equation.

$- x = - \sqrt{3} - 4$

Divide each term in $- x = - \sqrt{3} - 4$ by $- 1$ and simplify.

Divide each term in $- x = - \sqrt{3} - 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \sqrt{3}}{- 1} + \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \sqrt{3}}{- 1} + \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{3}}{- 1} + \frac{- 4}{- 1}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{\sqrt{3}}{1} + \frac{- 4}{- 1}$

Divide $\sqrt{3}$ by $1$ .

$x = \sqrt{3} + \frac{- 4}{- 1}$

Divide $- 4$ by $- 1$ .

$x = \sqrt{3} + 4$

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

$x = - \sqrt{3} + 4, \sqrt{3} + 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt{3} + 4, \sqrt{3} + 4$

Decimal Form:

$x = 2.26794919 \dots, 5.73205080 \dots$

Solve Using the Square Root Property 9(4-x)^2=27

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