Finite Math Examples

$x (x + 3) = 8$

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 $x (x + 3)$ .

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Step 1.1.1.1

Apply the distributive property.

$x \cdot x + x \cdot 3 = 8$

Step 1.1.1.2

Simplify the expression.

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Step 1.1.1.2.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 = 8$

Step 1.1.1.2.2

Move $3$ to the left of $x$ .

$x^{2} + 3 x = 8$

Step 1.2

Subtract $8$ from both sides of the equation.

$x^{2} + 3 x - 8 = 0$

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 $c$ .

$3^{2} - 4 (1 \cdot - 8)$

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 $3$ to the power of $2$ .

$9 - 4 (1 \cdot - 8)$

Step 4.1.2

Multiply $- 4 (1 \cdot - 8)$ .

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Step 4.1.2.1

Multiply $- 8$ by $1$ .

$9 - 4 \cdot - 8$

Step 4.1.2.2

Multiply $- 4$ by $- 8$ .

$9 + 32$

Step 4.2

Add $9$ and $32$ .

$41$