Pre-Algebra Examples

$- 9 {(x - 3)}^{2} = - 7$

Step 1

Divide each term in $- 9 {(x - 3)}^{2} = - 7$ by $- 9$ and simplify.

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Step 1.1

Divide each term in $- 9 {(x - 3)}^{2} = - 7$ by $- 9$ .

$\frac{- 9 {(x - 3)}^{2}}{- 9} = \frac{- 7}{- 9}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 9$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 9 {(x - 3)}^{2}}{- 9} = \frac{- 7}{- 9}$

Step 1.2.1.2

Divide ${(x - 3)}^{2}$ by $1$ .

${(x - 3)}^{2} = \frac{- 7}{- 9}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Dividing two negative values results in a positive value.

${(x - 3)}^{2} = \frac{7}{9}$

Step 2

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

$x - 3 = \pm \sqrt{\frac{7}{9}}$

Step 3

Simplify $\pm \sqrt{\frac{7}{9}}$ .

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Step 3.1

Rewrite $\sqrt{\frac{7}{9}}$ as $\frac{\sqrt{7}}{\sqrt{9}}$ .

$x - 3 = \pm \frac{\sqrt{7}}{\sqrt{9}}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Rewrite $9$ as $3^{2}$ .

$x - 3 = \pm \frac{\sqrt{7}}{\sqrt{3^{2}}}$

Step 3.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x - 3 = \pm \frac{\sqrt{7}}{3}$

Step 4

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

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Step 4.1

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

$x - 3 = \frac{\sqrt{7}}{3}$

Step 4.2

Add $3$ to both sides of the equation.

$x = \frac{\sqrt{7}}{3} + 3$

Step 4.3

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

$x - 3 = - \frac{\sqrt{7}}{3}$

Step 4.4

Add $3$ to both sides of the equation.

$x = - \frac{\sqrt{7}}{3} + 3$

Step 4.5

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

$x = \frac{\sqrt{7}}{3} + 3, - \frac{\sqrt{7}}{3} + 3$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{7}}{3} + 3, - \frac{\sqrt{7}}{3} + 3$

Decimal Form:

$x = 3.88191710 \dots, 2.11808289 \dots$