Trigonometry Examples

$x + {(y - 4)}^{2} = 0$

Step 1

Subtract ${(y - 4)}^{2}$ from both sides of the equation.

$x = - {(y - 4)}^{2}$

Step 2

Simplify both sides.

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Step 2.1

Rewrite ${(y - 4)}^{2}$ as $(y - 4) (y - 4)$ .

$x = - ((y - 4) (y - 4))$

Step 2.2

Expand $(y - 4) (y - 4)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$x = - (y (y - 4) - 4 (y - 4))$

Step 2.2.2

Apply the distributive property.

$x = - (y \cdot y + y \cdot - 4 - 4 (y - 4))$

Step 2.2.3

Apply the distributive property.

$x = - (y \cdot y + y \cdot - 4 - 4 y - 4 \cdot - 4)$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $y$ by $y$ .

$x = - (y^{2} + y \cdot - 4 - 4 y - 4 \cdot - 4)$

Step 2.3.1.2

Move $- 4$ to the left of $y$ .

$x = - (y^{2} - 4 \cdot y - 4 y - 4 \cdot - 4)$

Step 2.3.1.3

Multiply $- 4$ by $- 4$ .

$x = - (y^{2} - 4 y - 4 y + 16)$

Step 2.3.2

Subtract $4 y$ from $- 4 y$ .

$x = - (y^{2} - 8 y + 16)$

Step 2.4

Apply the distributive property.

$x = - y^{2} - (- 8 y) - 1 \cdot 16$

Step 2.5

Simplify.

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Step 2.5.1

Multiply $- 8$ by $- 1$ .

$x = - y^{2} + 8 y - 1 \cdot 16$

Step 2.5.2

Multiply $- 1$ by $16$ .

$x = - y^{2} + 8 y - 16$