Algebra Examples

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

Step 1

Move all terms not containing $k$ to the right side of the equation.

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Step 1.1

Subtract $2 x^{2}$ from both sides of the equation.

$- 8 x + 2 k = - 2 x^{2}$

Step 1.2

Add $8 x$ to both sides of the equation.

$2 k = - 2 x^{2} + 8 x$

Step 2

Divide each term in $2 k = - 2 x^{2} + 8 x$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 k = - 2 x^{2} + 8 x$ by $2$ .

$\frac{2 k}{2} = \frac{- 2 x^{2}}{2} + \frac{8 x}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 k}{2} = \frac{- 2 x^{2}}{2} + \frac{8 x}{2}$

Step 2.2.1.2

Divide $k$ by $1$ .

$k = \frac{- 2 x^{2}}{2} + \frac{8 x}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $- 2$ and $2$ .

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Step 2.3.1.1.1

Factor $2$ out of $- 2 x^{2}$ .

$k = \frac{2 (- x^{2})}{2} + \frac{8 x}{2}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $2$ .

$k = \frac{2 (- x^{2})}{2 (1)} + \frac{8 x}{2}$

Step 2.3.1.1.2.2

Cancel the common factor.

$k = \frac{2 (- x^{2})}{2 \cdot 1} + \frac{8 x}{2}$

Step 2.3.1.1.2.3

Rewrite the expression.

$k = \frac{- x^{2}}{1} + \frac{8 x}{2}$

Step 2.3.1.1.2.4

Divide $- x^{2}$ by $1$ .

$k = - x^{2} + \frac{8 x}{2}$

Step 2.3.1.2

Cancel the common factor of $8$ and $2$ .

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Step 2.3.1.2.1

Factor $2$ out of $8 x$ .

$k = - x^{2} + \frac{2 (4 x)}{2}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $2$ .

$k = - x^{2} + \frac{2 (4 x)}{2 (1)}$

Step 2.3.1.2.2.2

Cancel the common factor.

$k = - x^{2} + \frac{2 (4 x)}{2 \cdot 1}$

Step 2.3.1.2.2.3

Rewrite the expression.

$k = - x^{2} + \frac{4 x}{1}$

Step 2.3.1.2.2.4

Divide $4 x$ by $1$ .

$k = - x^{2} + 4 x$

Step 3

To rewrite as a function of $x$ , write the equation so that $k$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - x^{2} + 4 x$