Finite Math Examples

$a (- 21 - a) = 396$

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 $a (- 21 - a)$ .

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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.

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

Step 1.1.1.1.2

Reorder.

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Step 1.1.1.1.2.1

Move $- 21$ to the left of $a$ .

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

Step 1.1.1.1.2.2

Rewrite using the commutative property of multiplication.

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

Step 1.1.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 1.1.1.2.1

Move $a$ .

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

Step 1.1.1.2.2

Multiply $a$ by $a$ .

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

Step 1.2

Subtract $396$ from both sides of the equation.

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

Step 2

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

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

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

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

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 $- 21$ to the power of $2$ .

$441 - 4 (- - 396)$

Step 4.1.2

Multiply $- 4 (- - 396)$ .

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Step 4.1.2.1

Multiply $- 1$ by $- 396$ .

$441 - 4 \cdot 396$

Step 4.1.2.2

Multiply $- 4$ by $396$ .

$441 - 1584$

Step 4.2

Subtract $1584$ from $441$ .

$- 1143$