Algebra Examples

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

Step 1

Simplify $2 (x^{2} - 1) + 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 x^{2} + 2 \cdot - 1 + 1 = 1$

Step 1.1.2

Multiply $2$ by $- 1$ .

$2 x^{2} - 2 + 1 = 1$

Step 1.2

Add $- 2$ and $1$ .

$2 x^{2} - 1 = 1$

Step 2

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

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Step 2.1

Add $1$ to both sides of the equation.

$2 x^{2} = 1 + 1$

Step 2.2

Add $1$ and $1$ .

$2 x^{2} = 2$

Step 3

Divide each term in $2 x^{2} = 2$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x^{2} = 2$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{2}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{2}{2}$

Step 3.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{2}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $2$ by $2$ .

$x^{2} = 1$

Step 4

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

$x = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$x = \pm 1$

Step 6

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

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Step 6.1

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

$x = 1$

Step 6.2

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

$x = - 1$

Step 6.3

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

$x = 1, - 1$