Finite Math Examples

$2 z^{2} = 98$

Step 1

Divide each term in $2 z^{2} = 98$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 z^{2} = 98$ by $2$ .

$\frac{2 z^{2}}{2} = \frac{98}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 z^{2}}{2} = \frac{98}{2}$

Step 1.2.1.2

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

$z^{2} = \frac{98}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $98$ by $2$ .

$z^{2} = 49$

Step 2

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

$z = \pm \sqrt{49}$

Step 3

Simplify $\pm \sqrt{49}$ .

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Step 3.1

Rewrite $49$ as $7^{2}$ .

$z = \pm \sqrt{7^{2}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$z = \pm 7$

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.

$z = 7$

Step 4.2

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

$z = - 7$

Step 4.3

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

$z = 7, - 7$