Pre-Algebra Examples

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

Step 1

Add $3$ to both sides of the equation.

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

Step 2

Add $- 2$ and $3$ .

${(7 x - 2)}^{2} = 1$

Step 3

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

$7 x - 2 = \pm \sqrt{1}$

Step 4

Any root of $1$ is $1$ .

$7 x - 2 = \pm 1$

Step 5

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

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Step 5.1

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

$7 x - 2 = 1$

Step 5.2

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

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Step 5.2.1

Add $2$ to both sides of the equation.

$7 x = 1 + 2$

Step 5.2.2

Add $1$ and $2$ .

$7 x = 3$

Step 5.3

Divide each term in $7 x = 3$ by $7$ and simplify.

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Step 5.3.1

Divide each term in $7 x = 3$ by $7$ .

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

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $7$ .

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Step 5.3.2.1.1

Cancel the common factor.

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

Step 5.3.2.1.2

Divide $x$ by $1$ .

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

Step 5.4

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

$7 x - 2 = - 1$

Step 5.5

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

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Step 5.5.1

Add $2$ to both sides of the equation.

$7 x = - 1 + 2$

Step 5.5.2

Add $- 1$ and $2$ .

$7 x = 1$

Step 5.6

Divide each term in $7 x = 1$ by $7$ and simplify.

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Step 5.6.1

Divide each term in $7 x = 1$ by $7$ .

$\frac{7 x}{7} = \frac{1}{7}$

Step 5.6.2

Simplify the left side.

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Step 5.6.2.1

Cancel the common factor of $7$ .

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Step 5.6.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{1}{7}$

Step 5.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{7}$

Step 5.7

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

$x = \frac{3}{7}, \frac{1}{7}$