Finite Math Examples

$4 d = d^{2} - 45$

Step 1

Subtract $d^{2}$ from both sides of the equation.

$4 d - d^{2} = - 45$

Step 2

Add $45$ to both sides of the equation.

$4 d - d^{2} + 45 = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

Factor $- 1$ out of $4 d - d^{2} + 45$ .

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Step 3.1.1

Reorder $4 d$ and $- d^{2}$ .

$- d^{2} + 4 d + 45 = 0$

Step 3.1.2

Factor $- 1$ out of $- d^{2}$ .

$- (d^{2}) + 4 d + 45 = 0$

Step 3.1.3

Factor $- 1$ out of $4 d$ .

$- (d^{2}) - (- 4 d) + 45 = 0$

Step 3.1.4

Rewrite $45$ as $- 1 (- 45)$ .

$- (d^{2}) - (- 4 d) - 1 \cdot - 45 = 0$

Step 3.1.5

Factor $- 1$ out of $- (d^{2}) - (- 4 d)$ .

$- (d^{2} - 4 d) - 1 \cdot - 45 = 0$

Step 3.1.6

Factor $- 1$ out of $- (d^{2} - 4 d) - 1 (- 45)$ .

$- (d^{2} - 4 d - 45) = 0$

Step 3.2

Factor.

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Step 3.2.1

Factor $d^{2} - 4 d - 45$ using the AC method.

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Step 3.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 45$ and whose sum is $- 4$ .

$- 9, 5$

Step 3.2.1.2

Write the factored form using these integers.

$- ((d - 9) (d + 5)) = 0$

Step 3.2.2

Remove unnecessary parentheses.

$- (d - 9) (d + 5) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$d - 9 = 0$

$d + 5 = 0$

Step 5

Set $d - 9$ equal to $0$ and solve for $d$ .

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Step 5.1

Set $d - 9$ equal to $0$ .

$d - 9 = 0$

Step 5.2

Add $9$ to both sides of the equation.

$d = 9$

Step 6

Set $d + 5$ equal to $0$ and solve for $d$ .

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Step 6.1

Set $d + 5$ equal to $0$ .

$d + 5 = 0$

Step 6.2

Subtract $5$ from both sides of the equation.

$d = - 5$

Step 7

The final solution is all the values that make $- (d - 9) (d + 5) = 0$ true.

$d = 9, - 5$