Finite Math Examples

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

Step 1

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

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Step 1.1

Add $7$ to both sides of the equation.

$2 x^{2} = 3 + 7$

Step 1.2

Add $3$ and $7$ .

$2 x^{2} = 10$

Step 2

Divide each term in $2 x^{2} = 10$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 x^{2} = 10$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{10}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{10}{2}$

Step 2.2.1.2

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

$x^{2} = \frac{10}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $10$ by $2$ .

$x^{2} = 5$

Step 3

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

$x = \pm \sqrt{5}$

Step 4

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

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Step 4.1

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

$x = \sqrt{5}$

Step 4.2

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

$x = - \sqrt{5}$

Step 4.3

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

$x = \sqrt{5}, - \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$