Algebra Examples

$x (2 x - 3) + 5 = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$x (2 x) + x \cdot - 3 + 5 = 0$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 3 + 5 = 0$

Step 1.1.3

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

$2 x \cdot x - 3 \cdot x + 5 = 0$

Step 1.1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.4.1

Move $x$ .

$2 (x \cdot x) - 3 \cdot x + 5 = 0$

Step 1.1.4.2

Multiply $x$ by $x$ .

$2 x^{2} - 3 \cdot x + 5 = 0$

$2 x^{2} - 3 x + 5 = 0$

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 $c$ .

${(- 3)}^{2} - 4 (2 \cdot 5)$

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 $2$ .

$9 - 4 (2 \cdot 5)$

Step 4.1.2

Multiply $- 4 (2 \cdot 5)$ .

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Step 4.1.2.1

Multiply $2$ by $5$ .

$9 - 4 \cdot 10$

Step 4.1.2.2

Multiply $- 4$ by $10$ .

$9 - 40$

Step 4.2

Subtract $40$ from $9$ .

$- 31$