Linear Algebra Examples

- x (4 x + 3) = 0

$- x (4 x + 3) = 0$

Step 1

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

x = 0

$x = 0$

4 x + 3 = 0

$4 x + 3 = 0$

Step 2

Set

x

$x$ equal to

0

$0$ .

x = 0

$x = 0$

Step 3

Set

4 x + 3

$4 x + 3$ equal to

0

$0$ and solve for

x

$x$ .

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Step 3.1

Set

4 x + 3

$4 x + 3$ equal to

0

$0$ .

4 x + 3 = 0

$4 x + 3 = 0$

Step 3.2

Solve

4 x + 3 = 0

$4 x + 3 = 0$ for

x

$x$ .

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Step 3.2.1

Subtract

3

$3$ from both sides of the equation.

4 x = - 3

$4 x = - 3$

Step 3.2.2

Divide each term in

4 x = - 3

$4 x = - 3$ by

4

$4$ and simplify.

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Step 3.2.2.1

Divide each term in

4 x = - 3

$4 x = - 3$ by

4

$4$ .

\frac{4 x}{4} = \frac{- 3}{4}

$\frac{4 x}{4} = \frac{- 3}{4}$

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of

4

$4$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3}{4}$

Step 3.2.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{- 3}{4}$

$x = \frac{- 3}{4}$

$x = \frac{- 3}{4}$

Step 3.2.2.3

Simplify the right side.

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Step 3.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

$x = - \frac{3}{4}$

$x = - \frac{3}{4}$

$x = - \frac{3}{4}$

$x = - \frac{3}{4}$

Step 4

The final solution is all the values that make

$- x (4 x + 3) = 0$ true.

$x = 0, - \frac{3}{4}$

Step 5

The domain is the set of all valid

$x$ values.

${x | x = 0, - \frac{3}{4}}$

Step 6

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$