Precalculus Examples

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

Step 1

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

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

Step 2

Simplify $\pm \sqrt{9}$ .

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Step 2.1

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

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

Step 2.2

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

$7 x - 3 = \pm 3$

Step 3

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

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Step 3.1

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

$7 x - 3 = 3$

Step 3.2

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

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Step 3.2.1

Add $3$ to both sides of the equation.

$7 x = 3 + 3$

Step 3.2.2

Add $3$ and $3$ .

$7 x = 6$

Step 3.3

Divide each term in $7 x = 6$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 x = 6$ by $7$ .

$\frac{7 x}{7} = \frac{6}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{6}{7}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{7}$

Step 3.4

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

$7 x - 3 = - 3$

Step 3.5

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

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Step 3.5.1

Add $3$ to both sides of the equation.

$7 x = - 3 + 3$

Step 3.5.2

Add $- 3$ and $3$ .

$7 x = 0$

Step 3.6

Divide each term in $7 x = 0$ by $7$ and simplify.

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Step 3.6.1

Divide each term in $7 x = 0$ by $7$ .

$\frac{7 x}{7} = \frac{0}{7}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $7$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{0}{7}$

Step 3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{7}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $0$ by $7$ .

$x = 0$

Step 3.7

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

$x = \frac{6}{7}, 0$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{7}, 0$

Decimal Form:

$x = 0.\overline{857142}, 0$