Algebra Examples

$2 x (x + 5) = 4$

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $2 x (x + 5)$ .

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Step 1.1.1.1

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 5 = 4$

Step 1.1.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 5 = 4$

Step 1.1.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 5 = 4$

Step 1.1.1.3

Multiply $5$ by $2$ .

$2 x^{2} + 10 x = 4$

Step 1.2

Subtract $4$ from both sides of the equation.

$2 x^{2} + 10 x - 4 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 2$ , $b = 10$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (2 \cdot - 4)}}{2 \cdot 2}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 2 \cdot - 4}}{2 \cdot 2}$

Step 4.1.2

Multiply $- 4 \cdot 2 \cdot - 4$ .

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Step 4.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 8 \cdot - 4}}{2 \cdot 2}$

Step 4.1.2.2

Multiply $- 8$ by $- 4$ .

$x = \frac{- 10 \pm \sqrt{100 + 32}}{2 \cdot 2}$

Step 4.1.3

Add $100$ and $32$ .

$x = \frac{- 10 \pm \sqrt{132}}{2 \cdot 2}$

Step 4.1.4

Rewrite $132$ as $2^{2} \cdot 33$ .

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Step 4.1.4.1

Factor $4$ out of $132$ .

$x = \frac{- 10 \pm \sqrt{4 (33)}}{2 \cdot 2}$

Step 4.1.4.2

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

$x = \frac{- 10 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 2}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{- 10 \pm 2 \sqrt{33}}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$x = \frac{- 10 \pm 2 \sqrt{33}}{4}$

Step 4.3

Simplify $\frac{- 10 \pm 2 \sqrt{33}}{4}$ .

$x = \frac{- 5 \pm \sqrt{33}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 5 \pm \sqrt{33}}{2}$

Decimal Form:

$x = 0.37228132 \dots, - 5.37228132 \dots$