Algebra Examples

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

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 $2 (6 - x)$ .

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Multiply.

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Step 1.1.1.2.1

Multiply $2$ by $6$ .

$12 + 2 (- x) = x (x + 5)$

Step 1.1.1.2.2

Multiply $- 1$ by $2$ .

$12 - 2 x = x (x + 5)$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $x (x + 5)$ .

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Step 1.2.1.1

Apply the distributive property.

$12 - 2 x = x \cdot x + x \cdot 5$

Step 1.2.1.2

Simplify the expression.

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Step 1.2.1.2.1

Multiply $x$ by $x$ .

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

Step 1.2.1.2.2

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

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

Step 1.3

Move all the expressions to the left side of the equation.

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Step 1.3.1

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

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

Step 1.3.2

Subtract $5 x$ from both sides of the equation.

$12 - 2 x - x^{2} - 5 x = 0$

Step 1.4

Subtract $5 x$ from $- 2 x$ .

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

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 $a = - 1$ , $b = - 7$ , 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 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

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

Step 4.1.2

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

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Step 4.1.2.1

Multiply $- 4$ by $- 1$ .

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

Step 4.1.2.2

Multiply $4$ by $12$ .

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

Step 4.1.3

Add $49$ and $48$ .

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

Step 4.2

Multiply $2$ by $- 1$ .

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

Step 4.3

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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