Pre-Algebra Examples

$9 - x (2 x - 8) = 2 - 3 x$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$9 - x (2 x) - x \cdot - 8 = 2 - 3 x$

Step 1.2

Rewrite using the commutative property of multiplication.

$9 - 1 \cdot 2 x \cdot x - x \cdot - 8 = 2 - 3 x$

Step 1.3

Multiply $- 8$ by $- 1$ .

$9 - 1 \cdot 2 x \cdot x + 8 x = 2 - 3 x$

Step 1.4

Simplify each term.

Tap for more steps...

Step 1.4.1

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

Tap for more steps...

Step 1.4.1.1

Move $x$ .

$9 - 1 \cdot 2 (x \cdot x) + 8 x = 2 - 3 x$

Step 1.4.1.2

Multiply $x$ by $x$ .

$9 - 1 \cdot 2 x^{2} + 8 x = 2 - 3 x$

Step 1.4.2

Multiply $- 1$ by $2$ .

$9 - 2 x^{2} + 8 x = 2 - 3 x$

Step 2

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

Tap for more steps...

Step 2.1

Add $3 x$ to both sides of the equation.

$9 - 2 x^{2} + 8 x + 3 x = 2$

Step 2.2

Add $8 x$ and $3 x$ .

$9 - 2 x^{2} + 11 x = 2$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $2$ from both sides of the equation.

$9 - 2 x^{2} + 11 x - 2 = 0$

Step 3.2

Subtract $2$ from $9$ .

$- 2 x^{2} + 11 x + 7 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = - 2$ , $b = 11$ , and $c = 7$ into the quadratic formula and solve for $x$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (- 2 \cdot 7)}}{2 \cdot - 2}$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Simplify the numerator.

Tap for more steps...

Step 6.1.1

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot - 2 \cdot 7}}{2 \cdot - 2}$

Step 6.1.2

Multiply $- 4 \cdot - 2 \cdot 7$ .

Tap for more steps...

Step 6.1.2.1

Multiply $- 4$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{121 + 8 \cdot 7}}{2 \cdot - 2}$

Step 6.1.2.2

Multiply $8$ by $7$ .

$x = \frac{- 11 \pm \sqrt{121 + 56}}{2 \cdot - 2}$

Step 6.1.3

Add $121$ and $56$ .

$x = \frac{- 11 \pm \sqrt{177}}{2 \cdot - 2}$

Step 6.2

Multiply $2$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{177}}{- 4}$

Step 6.3

Simplify $\frac{- 11 \pm \sqrt{177}}{- 4}$ .

$x = \frac{11 \pm \sqrt{177}}{4}$

Step 7

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Tap for more steps...

Step 7.1

Simplify the numerator.

Tap for more steps...

Step 7.1.1

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot - 2 \cdot 7}}{2 \cdot - 2}$

Step 7.1.2

Multiply $- 4 \cdot - 2 \cdot 7$ .

Tap for more steps...

Step 7.1.2.1

Multiply $- 4$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{121 + 8 \cdot 7}}{2 \cdot - 2}$

Step 7.1.2.2

Multiply $8$ by $7$ .

$x = \frac{- 11 \pm \sqrt{121 + 56}}{2 \cdot - 2}$

Step 7.1.3

Add $121$ and $56$ .

$x = \frac{- 11 \pm \sqrt{177}}{2 \cdot - 2}$

Step 7.2

Multiply $2$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{177}}{- 4}$

Step 7.3

Simplify $\frac{- 11 \pm \sqrt{177}}{- 4}$ .

$x = \frac{11 \pm \sqrt{177}}{4}$

Step 7.4

Change the $\pm$ to $+$ .

$x = \frac{11 + \sqrt{177}}{4}$

Step 8

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot - 2 \cdot 7}}{2 \cdot - 2}$

Step 8.1.2

Multiply $- 4 \cdot - 2 \cdot 7$ .

Tap for more steps...

Step 8.1.2.1

Multiply $- 4$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{121 + 8 \cdot 7}}{2 \cdot - 2}$

Step 8.1.2.2

Multiply $8$ by $7$ .

$x = \frac{- 11 \pm \sqrt{121 + 56}}{2 \cdot - 2}$

Step 8.1.3

Add $121$ and $56$ .

$x = \frac{- 11 \pm \sqrt{177}}{2 \cdot - 2}$

Step 8.2

Multiply $2$ by $- 2$ .

$x = \frac{- 11 \pm \sqrt{177}}{- 4}$

Step 8.3

Simplify $\frac{- 11 \pm \sqrt{177}}{- 4}$ .

$x = \frac{11 \pm \sqrt{177}}{4}$

Step 8.4

Change the $\pm$ to $-$ .

$x = \frac{11 - \sqrt{177}}{4}$

Step 9

The final answer is the combination of both solutions.

$x = \frac{11 + \sqrt{177}}{4}, \frac{11 - \sqrt{177}}{4}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11 + \sqrt{177}}{4}, \frac{11 - \sqrt{177}}{4}$

Decimal Form:

$x = 6.07603367 \dots, - 0.57603367 \dots$