Algebra Examples

$2 (6 - x) = x (x + 5)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x (x + 5) = 2 (6 - x)$

Step 2

Simplify $x (x + 5)$ .

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Step 2.1

Rewrite.

$0 + 0 + x (x + 5) = 2 (6 - x)$

Step 2.2

Simplify by adding zeros.

$x (x + 5) = 2 (6 - x)$

Step 2.3

Apply the distributive property.

$x \cdot x + x \cdot 5 = 2 (6 - x)$

Step 2.4

Simplify the expression.

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Step 2.4.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 5 = 2 (6 - x)$

Step 2.4.2

Move $5$ to the left of $x$ .

$x^{2} + 5 x = 2 (6 - x)$

Step 3

Simplify $2 (6 - x)$ .

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Step 3.1

Apply the distributive property.

$x^{2} + 5 x = 2 \cdot 6 + 2 (- x)$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $2$ by $6$ .

$x^{2} + 5 x = 12 + 2 (- x)$

Step 3.2.2

Multiply $- 1$ by $2$ .

$x^{2} + 5 x = 12 - 2 x$

Step 4

Move all terms containing $x$ to the left side of the equation.

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Step 4.1

Add $2 x$ to both sides of the equation.

$x^{2} + 5 x + 2 x = 12$

Step 4.2

Add $5 x$ and $2 x$ .

$x^{2} + 7 x = 12$

Step 5

Subtract $12$ from both sides of the equation.

$x^{2} + 7 x - 12 = 0$

Step 6

Use the quadratic formula to find the solutions.

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

Step 7

Substitute the values $a = 1$ , $b = 7$ , and $c = - 12$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot - 12)}}{2 \cdot 1}$

Step 8

Simplify.

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot - 12}}{2 \cdot 1}$

Step 8.1.2

Multiply $- 4 \cdot 1 \cdot - 12$ .

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Step 8.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 12}}{2 \cdot 1}$

Step 8.1.2.2

Multiply $- 4$ by $- 12$ .

$x = \frac{- 7 \pm \sqrt{49 + 48}}{2 \cdot 1}$

Step 8.1.3

Add $49$ and $48$ .

$x = \frac{- 7 \pm \sqrt{97}}{2 \cdot 1}$

Step 8.2

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm \sqrt{97}}{2}$

Step 9

The final answer is the combination of both solutions.

$x = - \frac{7 - \sqrt{97}}{2}, - \frac{7 + \sqrt{97}}{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7 - \sqrt{97}}{2}, - \frac{7 + \sqrt{97}}{2}$

Decimal Form:

$x = 1.42442890 \dots, - 8.42442890 \dots$