Calculus Examples

$z^{2} - 6 x + 10 = 0$

Step 1

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

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Step 1.1

Add $6 x$ to both sides of the equation.

$z^{2} + 10 = 6 x$

Step 1.2

Subtract $10$ from both sides of the equation.

$z^{2} = 6 x - 10$

Step 2

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

$z = \pm \sqrt{6 x - 10}$

Step 3

Factor $2$ out of $6 x - 10$ .

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Step 3.1

Factor $2$ out of $6 x$ .

$z = \pm \sqrt{2 (3 x) - 10}$

Step 3.2

Factor $2$ out of $- 10$ .

$z = \pm \sqrt{2 (3 x) + 2 (- 5)}$

Step 3.3

Factor $2$ out of $2 (3 x) + 2 (- 5)$ .

$z = \pm \sqrt{2 (3 x - 5)}$

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.

$z = \sqrt{2 (3 x - 5)}$

Step 4.2

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

$z = - \sqrt{2 (3 x - 5)}$

Step 4.3

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

$z = \sqrt{2 (3 x - 5)}$

$z = - \sqrt{2 (3 x - 5)}$

$z = \sqrt{2 (3 x - 5)}$

$z = - \sqrt{2 (3 x - 5)}$