Finite Math Examples

a (- 21 - a) = 396

$a (- 21 - a) = 396$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify

a (- 21 - a)

$a (- 21 - a)$ .

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Step 1.1.1.1

Simplify by multiplying through.

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Step 1.1.1.1.1

Apply the distributive property.

a \cdot - 21 + a (- a) = 396

$a \cdot - 21 + a (- a) = 396$

Step 1.1.1.1.2

Reorder.

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Step 1.1.1.1.2.1

Move

- 21

$- 21$ to the left of

a

$a$ .

- 21 \cdot a + a (- a) = 396

$- 21 \cdot a + a (- a) = 396$

Step 1.1.1.1.2.2

Rewrite using the commutative property of multiplication.

- 21 \cdot a - a \cdot a = 396

$- 21 \cdot a - a \cdot a = 396$

- 21 \cdot a - a \cdot a = 396

$- 21 \cdot a - a \cdot a = 396$

- 21 \cdot a - a \cdot a = 396

$- 21 \cdot a - a \cdot a = 396$

Step 1.1.1.2

Multiply

a

$a$ by

a

$a$ by adding the exponents.

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Step 1.1.1.2.1

Move

a

$a$ .

- 21 a - (a \cdot a) = 396

$- 21 a - (a \cdot a) = 396$

Step 1.1.1.2.2

Multiply

a

$a$ by

a

$a$ .

- 21 a - a^{2} = 396

$- 21 a - a^{2} = 396$

- 21 a - a^{2} = 396

$- 21 a - a^{2} = 396$

- 21 a - a^{2} = 396

$- 21 a - a^{2} = 396$

- 21 a - a^{2} = 396

$- 21 a - a^{2} = 396$

Step 1.2

Subtract

396

$396$ from both sides of the equation.

- 21 a - a^{2} - 396 = 0

$- 21 a - a^{2} - 396 = 0$

- 21 a - a^{2} - 396 = 0

$- 21 a - a^{2} - 396 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b^{2} - 4 (a c)

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of

a

$a$ ,

b

$b$ , and

c

$c$ .

{(- 21)}^{2} - 4 (- - 396)

${(- 21)}^{2} - 4 (- - 396)$

Step 4

Evaluate the result to find the discriminant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Raise

- 21

$- 21$ to the power of

2

$2$ .

441 - 4 (- - 396)

$441 - 4 (- - 396)$

Step 4.1.2

Multiply

- 4 (- - 396)

$- 4 (- - 396)$ .

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Step 4.1.2.1

Multiply

- 1

$- 1$ by

- 396

$- 396$ .

441 - 4 \cdot 396

$441 - 4 \cdot 396$

Step 4.1.2.2

Multiply

- 4

$- 4$ by

396

$396$ .

441 - 1584

$441 - 1584$

441 - 1584

$441 - 1584$

441 - 1584

$441 - 1584$

Step 4.2

Subtract

1584

$1584$ from

441

$441$ .

- 1143

$- 1143$

- 1143

$- 1143$