Algebra Examples

$2 x^{2} - \frac{2}{3} = 5 \frac{1}{3}$

Step 1

Simplify the right side.

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Step 1.1

Convert $5 \frac{1}{3}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$2 x^{2} - \frac{2}{3} = 5 + \frac{1}{3}$

Step 1.1.2

Add $5$ and $\frac{1}{3}$ .

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Step 1.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 x^{2} - \frac{2}{3} = 5 \cdot \frac{3}{3} + \frac{1}{3}$

Step 1.1.2.2

Combine $5$ and $\frac{3}{3}$ .

$2 x^{2} - \frac{2}{3} = \frac{5 \cdot 3}{3} + \frac{1}{3}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$2 x^{2} - \frac{2}{3} = \frac{5 \cdot 3 + 1}{3}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $5$ by $3$ .

$2 x^{2} - \frac{2}{3} = \frac{15 + 1}{3}$

Step 1.1.2.4.2

Add $15$ and $1$ .

$2 x^{2} - \frac{2}{3} = \frac{16}{3}$

Step 2

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

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Step 2.1

Add $\frac{2}{3}$ to both sides of the equation.

$2 x^{2} = \frac{16}{3} + \frac{2}{3}$

Step 2.2

Combine the numerators over the common denominator.

$2 x^{2} = \frac{16 + 2}{3}$

Step 2.3

Add $16$ and $2$ .

$2 x^{2} = \frac{18}{3}$

Step 2.4

Divide $18$ by $3$ .

$2 x^{2} = 6$

Step 3

Divide each term in $2 x^{2} = 6$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x^{2} = 6$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{6}{2}$

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.

$\frac{2 x^{2}}{2} = \frac{6}{2}$

Step 3.2.1.2

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

$x^{2} = \frac{6}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $6$ by $2$ .

$x^{2} = 3$

Step 4

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

$x = \pm \sqrt{3}$

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.

$x = \sqrt{3}$

Step 5.2

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

$x = - \sqrt{3}$

Step 5.3

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

$x = \sqrt{3}, - \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3}, - \sqrt{3}$

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$