Precalculus Examples

$x = - 2 {(y - 5)}^{2} - 5$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $- 2 {(y - 5)}^{2} - 5 = x$ .

$- 2 {(y - 5)}^{2} - 5 = x$

Step 1.2

Add $5$ to both sides of the equation.

$- 2 {(y - 5)}^{2} = x + 5$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$x = a x^{2} + b x + c$

Step 3

Simplify each term.

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Step 3.1

Rewrite ${(y - 5)}^{2}$ as $(y - 5) (y - 5)$ .

$x = - 2 ((y - 5) (y - 5)) - 5$

Step 3.2

Expand $(y - 5) (y - 5)$ using the FOIL Method.

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Step 3.2.1

Apply the distributive property.

$x = - 2 (y (y - 5) - 5 (y - 5)) - 5$

Step 3.2.2

Apply the distributive property.

$x = - 2 (y \cdot y + y \cdot - 5 - 5 (y - 5)) - 5$

Step 3.2.3

Apply the distributive property.

$x = - 2 (y \cdot y + y \cdot - 5 - 5 y - 5 \cdot - 5) - 5$

Step 3.3

Simplify and combine like terms.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply $y$ by $y$ .

$x = - 2 (y^{2} + y \cdot - 5 - 5 y - 5 \cdot - 5) - 5$

Step 3.3.1.2

Move $- 5$ to the left of $y$ .

$x = - 2 (y^{2} - 5 \cdot y - 5 y - 5 \cdot - 5) - 5$

Step 3.3.1.3

Multiply $- 5$ by $- 5$ .

$x = - 2 (y^{2} - 5 y - 5 y + 25) - 5$

Step 3.3.2

Subtract $5 y$ from $- 5 y$ .

$x = - 2 (y^{2} - 10 y + 25) - 5$

Step 3.4

Apply the distributive property.

$x = - 2 y^{2} - 2 (- 10 y) - 2 \cdot 25 - 5$

Step 3.5

Simplify.

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Step 3.5.1

Multiply $- 10$ by $- 2$ .

$x = - 2 y^{2} + 20 y - 2 \cdot 25 - 5$

Step 3.5.2

Multiply $- 2$ by $25$ .

$x = - 2 y^{2} + 20 y - 50 - 5$

Step 4

Subtract $5$ from $- 50$ .

$x = - 2 y^{2} + 20 y - 55$

Step 5