Algebra Examples

$132 = \frac{1}{2} \cdot (x (2 x + 2))$

Step 1

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

Tap for more steps...

Step 1.1

Simplify the right side.

Tap for more steps...

Step 1.1.1

Simplify $\frac{1}{2} \cdot (x (2 x + 2))$ .

Tap for more steps...

Step 1.1.1.1

Simplify by multiplying through.

Tap for more steps...

Step 1.1.1.1.1

Apply the distributive property.

$132 = \frac{1}{2} \cdot (x (2 x) + x \cdot 2)$

Step 1.1.1.1.2

Reorder.

Tap for more steps...

Step 1.1.1.1.2.1

Rewrite using the commutative property of multiplication.

$132 = \frac{1}{2} \cdot (2 x \cdot x + x \cdot 2)$

Step 1.1.1.1.2.2

Move $2$ to the left of $x$ .

$132 = \frac{1}{2} \cdot (2 x \cdot x + 2 \cdot x)$

Step 1.1.1.2

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

Tap for more steps...

Step 1.1.1.2.1

Move $x$ .

$132 = \frac{1}{2} \cdot (2 (x \cdot x) + 2 \cdot x)$

Step 1.1.1.2.2

Multiply $x$ by $x$ .

$132 = \frac{1}{2} \cdot (2 x^{2} + 2 \cdot x)$

$132 = \frac{1}{2} \cdot (2 x^{2} + 2 x)$

Step 1.1.1.3

Simplify terms.

Tap for more steps...

Step 1.1.1.3.1

Apply the distributive property.

$132 = \frac{1}{2} (2 x^{2}) + \frac{1}{2} (2 x)$

Step 1.1.1.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.1.3.2.1

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

$132 = \frac{1}{2} (2 (x^{2})) + \frac{1}{2} (2 x)$

Step 1.1.1.3.2.2

Cancel the common factor.

$132 = \frac{1}{2} (2 x^{2}) + \frac{1}{2} (2 x)$

Step 1.1.1.3.2.3

Rewrite the expression.

$132 = x^{2} + \frac{1}{2} (2 x)$

Step 1.1.1.3.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.1.3.3.1

Factor $2$ out of $2 x$ .

$132 = x^{2} + \frac{1}{2} (2 (x))$

Step 1.1.1.3.3.2

Cancel the common factor.

$132 = x^{2} + \frac{1}{2} (2 x)$

Step 1.1.1.3.3.3

Rewrite the expression.

$132 = x^{2} + x$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$132 - x^{2} = x$

Step 1.2.2

Subtract $x$ from both sides of the equation.

$132 - x^{2} - x = 0$

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 $a = - 1$ , $b = - 1$ , and $c = 132$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (- 1 \cdot 132)}}{2 \cdot - 1}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

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

$x = \frac{1 \pm \sqrt{1 - 4 \cdot - 1 \cdot 132}}{2 \cdot - 1}$

Step 4.1.2

Multiply $- 4 \cdot - 1 \cdot 132$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $- 1$ .

$x = \frac{1 \pm \sqrt{1 + 4 \cdot 132}}{2 \cdot - 1}$

Step 4.1.2.2

Multiply $4$ by $132$ .

$x = \frac{1 \pm \sqrt{1 + 528}}{2 \cdot - 1}$

Step 4.1.3

Add $1$ and $528$ .

$x = \frac{1 \pm \sqrt{529}}{2 \cdot - 1}$

Step 4.1.4

Rewrite $529$ as $23^{2}$ .

$x = \frac{1 \pm \sqrt{23^{2}}}{2 \cdot - 1}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{1 \pm 23}{2 \cdot - 1}$

Step 4.2

Multiply $2$ by $- 1$ .

$x = \frac{1 \pm 23}{- 2}$

Step 4.3

Move the negative in front of the fraction.

$x = - \frac{1 \pm 23}{2}$

Step 5

The final answer is the combination of both solutions.

$x = - 12, 11$