Basic Math Examples

$d^{2} + d {(d - 6)}^{2} = 676$

Step 1

Simplify $d^{2} + d {(d - 6)}^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(d - 6)}^{2}$ as $(d - 6) (d - 6)$ .

$d^{2} + d ((d - 6) (d - 6)) = 676$

Step 1.1.2

Expand $(d - 6) (d - 6)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$d^{2} + d (d (d - 6) - 6 (d - 6)) = 676$

Step 1.1.2.2

Apply the distributive property.

$d^{2} + d (d \cdot d + d \cdot - 6 - 6 (d - 6)) = 676$

Step 1.1.2.3

Apply the distributive property.

$d^{2} + d (d \cdot d + d \cdot - 6 - 6 d - 6 \cdot - 6) = 676$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $d$ by $d$ .

$d^{2} + d (d^{2} + d \cdot - 6 - 6 d - 6 \cdot - 6) = 676$

Step 1.1.3.1.2

Move $- 6$ to the left of $d$ .

$d^{2} + d (d^{2} - 6 \cdot d - 6 d - 6 \cdot - 6) = 676$

Step 1.1.3.1.3

Multiply $- 6$ by $- 6$ .

$d^{2} + d (d^{2} - 6 d - 6 d + 36) = 676$

Step 1.1.3.2

Subtract $6 d$ from $- 6 d$ .

$d^{2} + d (d^{2} - 12 d + 36) = 676$

Step 1.1.4

Apply the distributive property.

$d^{2} + d \cdot d^{2} + d (- 12 d) + d \cdot 36 = 676$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Multiply $d$ by $d^{2}$ by adding the exponents.

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Step 1.1.5.1.1

Multiply $d$ by $d^{2}$ .

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Step 1.1.5.1.1.1

Raise $d$ to the power of $1$ .

$d^{2} + d^{1} d^{2} + d (- 12 d) + d \cdot 36 = 676$

Step 1.1.5.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$d^{2} + d^{1 + 2} + d (- 12 d) + d \cdot 36 = 676$

Step 1.1.5.1.2

Add $1$ and $2$ .

$d^{2} + d^{3} + d (- 12 d) + d \cdot 36 = 676$

Step 1.1.5.2

Rewrite using the commutative property of multiplication.

$d^{2} + d^{3} - 12 d \cdot d + d \cdot 36 = 676$

Step 1.1.5.3

Move $36$ to the left of $d$ .

$d^{2} + d^{3} - 12 d \cdot d + 36 \cdot d = 676$

Step 1.1.6

Multiply $d$ by $d$ by adding the exponents.

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Step 1.1.6.1

Move $d$ .

$d^{2} + d^{3} - 12 (d \cdot d) + 36 \cdot d = 676$

Step 1.1.6.2

Multiply $d$ by $d$ .

$d^{2} + d^{3} - 12 d^{2} + 36 \cdot d = 676$

$d^{2} + d^{3} - 12 d^{2} + 36 d = 676$

Step 1.2

Subtract $12 d^{2}$ from $d^{2}$ .

$d^{3} - 11 d^{2} + 36 d = 676$

Step 2

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

$d \approx 12.46339297$

Step 3