Pre-Algebra Examples

${(1 - 2 x)}^{2} = 23$

Step 1

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

$1 - 2 x = \pm \sqrt{23}$

Step 2

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

Tap for more steps...

Step 2.1

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

$1 - 2 x = \sqrt{23}$

Step 2.2

Subtract $1$ from both sides of the equation.

$- 2 x = \sqrt{23} - 1$

Step 2.3

Divide each term in $- 2 x = \sqrt{23} - 1$ by $- 2$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $- 2 x = \sqrt{23} - 1$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{\sqrt{23}}{- 2} + \frac{- 1}{- 2}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{\sqrt{23}}{- 2} + \frac{- 1}{- 2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{23}}{- 2} + \frac{- 1}{- 2}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Simplify each term.

Tap for more steps...

Step 2.3.3.1.1

Move the negative in front of the fraction.

$x = - \frac{\sqrt{23}}{2} + \frac{- 1}{- 2}$

Step 2.3.3.1.2

Dividing two negative values results in a positive value.

$x = - \frac{\sqrt{23}}{2} + \frac{1}{2}$

Step 2.4

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

$1 - 2 x = - \sqrt{23}$

Step 2.5

Subtract $1$ from both sides of the equation.

$- 2 x = - \sqrt{23} - 1$

Step 2.6

Divide each term in $- 2 x = - \sqrt{23} - 1$ by $- 2$ and simplify.

Tap for more steps...

Step 2.6.1

Divide each term in $- 2 x = - \sqrt{23} - 1$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- \sqrt{23}}{- 2} + \frac{- 1}{- 2}$

Step 2.6.2

Simplify the left side.

Tap for more steps...

Step 2.6.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 2.6.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- \sqrt{23}}{- 2} + \frac{- 1}{- 2}$

Step 2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \sqrt{23}}{- 2} + \frac{- 1}{- 2}$

Step 2.6.3

Simplify the right side.

Tap for more steps...

Step 2.6.3.1

Simplify each term.

Tap for more steps...

Step 2.6.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{\sqrt{23}}{2} + \frac{- 1}{- 2}$

Step 2.6.3.1.2

Dividing two negative values results in a positive value.

$x = \frac{\sqrt{23}}{2} + \frac{1}{2}$

Step 2.7

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

$x = - \frac{\sqrt{23}}{2} + \frac{1}{2}, \frac{\sqrt{23}}{2} + \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\sqrt{23}}{2} + \frac{1}{2}, \frac{\sqrt{23}}{2} + \frac{1}{2}$

Decimal Form:

$x = - 1.89791576 \dots, 2.89791576 \dots$