Algebra Examples

$2 x^{2} - 4 x = 14$

Step 1

Divide each term in $2 x^{2} - 4 x = 14$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 x^{2} - 4 x = 14$ by $2$ .

$\frac{2 x^{2}}{2} + \frac{- 4 x}{2} = \frac{14}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Cancel the common factor of $2$ .

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Step 1.2.1.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{- 4 x}{2} = \frac{14}{2}$

Step 1.2.1.1.2

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

$x^{2} + \frac{- 4 x}{2} = \frac{14}{2}$

Step 1.2.1.2

Cancel the common factor of $- 4$ and $2$ .

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Step 1.2.1.2.1

Factor $2$ out of $- 4 x$ .

$x^{2} + \frac{2 (- 2 x)}{2} = \frac{14}{2}$

Step 1.2.1.2.2

Cancel the common factors.

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Step 1.2.1.2.2.1

Factor $2$ out of $2$ .

$x^{2} + \frac{2 (- 2 x)}{2 (1)} = \frac{14}{2}$

Step 1.2.1.2.2.2

Cancel the common factor.

$x^{2} + \frac{2 (- 2 x)}{2 \cdot 1} = \frac{14}{2}$

Step 1.2.1.2.2.3

Rewrite the expression.

$x^{2} + \frac{- 2 x}{1} = \frac{14}{2}$

Step 1.2.1.2.2.4

Divide $- 2 x$ by $1$ .

$x^{2} - 2 x = \frac{14}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $14$ by $2$ .

$x^{2} - 2 x = 7$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 1)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 2 x + {(- 1)}^{2} = 7 + {(- 1)}^{2}$

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Raise $- 1$ to the power of $2$ .

$x^{2} - 2 x + 1 = 7 + {(- 1)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $7 + {(- 1)}^{2}$ .

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Step 4.2.1.1

Raise $- 1$ to the power of $2$ .

$x^{2} - 2 x + 1 = 7 + 1$

Step 4.2.1.2

Add $7$ and $1$ .

$x^{2} - 2 x + 1 = 8$

Step 5

Factor the perfect trinomial square into ${(x - 1)}^{2}$ .

${(x - 1)}^{2} = 8$

Step 6

Solve the equation for $x$ .

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Step 6.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x - 1 = \pm \sqrt{8}$

Step 6.2

Simplify $\pm \sqrt{8}$ .

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Step 6.2.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 6.2.1.1

Factor $4$ out of $8$ .

$x - 1 = \pm \sqrt{4 (2)}$

Step 6.2.1.2

Rewrite $4$ as $2^{2}$ .

$x - 1 = \pm \sqrt{2^{2} \cdot 2}$

Step 6.2.2

Pull terms out from under the radical.

$x - 1 = \pm 2 \sqrt{2}$

Step 6.3

Add $1$ to both sides of the equation.

$x = \pm 2 \sqrt{2} + 1$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{2} + 1$

Decimal Form:

$x = 3.82842712 \dots, - 1.82842712 \dots$