Finite Math Examples

${(x - 2)}^{2} + (y + 1) = 16$

Step 1

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

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Step 1.1

Subtract $y$ from both sides of the equation.

${(x - 2)}^{2} + 1 = 16 - y$

Step 1.2

Subtract $1$ from both sides of the equation.

${(x - 2)}^{2} = 16 - y - 1$

Step 2

Subtract $1$ from $16$ .

${(x - 2)}^{2} = - y + 15$

Step 3

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

$x - 2 = \pm \sqrt{- y + 15}$

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.

$x - 2 = \sqrt{- y + 15}$

Step 4.2

Add $2$ to both sides of the equation.

$x = \sqrt{- y + 15} + 2$

Step 4.3

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

$x - 2 = - \sqrt{- y + 15}$

Step 4.4

Add $2$ to both sides of the equation.

$x = - \sqrt{- y + 15} + 2$

Step 4.5

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

$x = \sqrt{- y + 15} + 2$

$x = - \sqrt{- y + 15} + 2$

$x = \sqrt{- y + 15} + 2$

$x = - \sqrt{- y + 15} + 2$