Algebra Examples

$x^{2} + 3 x = - 2 x - 6$

Step 1

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

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Step 1.1

Move all the expressions to the left side of the equation.

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Step 1.1.1

Add $2 x$ to both sides of the equation.

$x^{2} + 3 x + 2 x = - 6$

Step 1.1.2

Add $6$ to both sides of the equation.

$x^{2} + 3 x + 2 x + 6 = 0$

Step 1.2

Add $3 x$ and $2 x$ .

$x^{2} + 5 x + 6 = 0$

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 $c$ .

$5^{2} - 4 (1 \cdot 6)$

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 $5$ to the power of $2$ .

$25 - 4 (1 \cdot 6)$

Step 4.1.2

Multiply $- 4 (1 \cdot 6)$ .

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Step 4.1.2.1

Multiply $6$ by $1$ .

$25 - 4 \cdot 6$

Step 4.1.2.2

Multiply $- 4$ by $6$ .

$25 - 24$

Step 4.2

Subtract $24$ from $25$ .

$1$