Linear Algebra Examples

$x = \frac{b + \sqrt{b^{2}} - 4 a c}{2 a}$

Step 1

Simplify $\frac{b + \sqrt{b^{2}} - 4 a c}{2 a}$ .

Tap for more steps...

Step 1.1

Simplify the numerator.

Tap for more steps...

Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b^{2}}$ as $b^{\frac{2}{2}}$ .

$x = \frac{b + b^{\frac{2}{2}} - 4 a c}{2 a}$

Step 1.1.2

Divide $2$ by $2$ .

$x = \frac{b + b^{1} - 4 a c}{2 a}$

Step 1.1.3

Simplify.

$x = \frac{b + b - 4 a c}{2 a}$

Step 1.1.4

Add $b$ and $b$ .

$x = \frac{2 b - 4 a c}{2 a}$

Step 1.1.5

Factor $2$ out of $2 b - 4 a c$ .

Tap for more steps...

Step 1.1.5.1

Factor $2$ out of $2 b$ .

$x = \frac{2 (b) - 4 a c}{2 a}$

Step 1.1.5.2

Factor $2$ out of $- 4 a c$ .

$x = \frac{2 (b) + 2 (- 2 a c)}{2 a}$

Step 1.1.5.3

Factor $2$ out of $2 (b) + 2 (- 2 a c)$ .

$x = \frac{2 (b - 2 a c)}{2 a}$

Step 1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$x = \frac{2 (b - 2 a c)}{2 a}$

Step 1.2.2

Rewrite the expression.

$x = \frac{b - 2 a c}{a}$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$