Basic Math Examples

$2 y^{3} - 12 y - 5 = {(y - 4)}^{2}$

Step 1

Simplify ${(y - 4)}^{2}$ .

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Step 1.1

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

$2 y^{3} - 12 y - 5 = (y - 4) (y - 4)$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$2 y^{3} - 12 y - 5 = y (y - 4) - 4 (y - 4)$

Step 1.2.2

Apply the distributive property.

$2 y^{3} - 12 y - 5 = y \cdot y + y \cdot - 4 - 4 (y - 4)$

Step 1.2.3

Apply the distributive property.

$2 y^{3} - 12 y - 5 = y \cdot y + y \cdot - 4 - 4 y - 4 \cdot - 4$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $y$ by $y$ .

$2 y^{3} - 12 y - 5 = y^{2} + y \cdot - 4 - 4 y - 4 \cdot - 4$

Step 1.3.1.2

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

$2 y^{3} - 12 y - 5 = y^{2} - 4 \cdot y - 4 y - 4 \cdot - 4$

Step 1.3.1.3

Multiply $- 4$ by $- 4$ .

$2 y^{3} - 12 y - 5 = y^{2} - 4 y - 4 y + 16$

Step 1.3.2

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

$2 y^{3} - 12 y - 5 = y^{2} - 8 y + 16$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$y \approx 2.69193395$

Step 3