Solve Using the Quadratic Formula x(9x+2)=6

$x (9 x + 2) = 6$

Step 1

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

Simplify the left side.

Simplify $x (9 x + 2)$ .

Simplify by multiplying through.

Apply the distributive property.

$x (9 x) + x \cdot 2 = 6$

Reorder.

Rewrite using the commutative property of multiplication.

$9 x \cdot x + x \cdot 2 = 6$

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

$9 x \cdot x + 2 \cdot x = 6$

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

Move $x$ .

$9 (x \cdot x) + 2 \cdot x = 6$

Multiply $x$ by $x$ .

$9 x^{2} + 2 \cdot x = 6$

$9 x^{2} + 2 x = 6$

Subtract $6$ from both sides of the equation.

$9 x^{2} + 2 x - 6 = 0$

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 $a = 9$ , $b = 2$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (9 \cdot - 6)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 9 \cdot - 6}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 6$ .

Multiply $- 4$ by $9$ .

$x = \frac{- 2 \pm \sqrt{4 - 36 \cdot - 6}}{2 \cdot 9}$

Multiply $- 36$ by $- 6$ .

$x = \frac{- 2 \pm \sqrt{4 + 216}}{2 \cdot 9}$

Add $4$ and $216$ .

$x = \frac{- 2 \pm \sqrt{220}}{2 \cdot 9}$

Rewrite $220$ as $2^{2} \cdot 55$ .

Factor $4$ out of $220$ .

$x = \frac{- 2 \pm \sqrt{4 (55)}}{2 \cdot 9}$

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

$x = \frac{- 2 \pm \sqrt{2^{2} \cdot 55}}{2 \cdot 9}$

Pull terms out from under the radical.

$x = \frac{- 2 \pm 2 \sqrt{55}}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{- 2 \pm 2 \sqrt{55}}{18}$

Simplify $\frac{- 2 \pm 2 \sqrt{55}}{18}$ .

$x = \frac{- 1 \pm \sqrt{55}}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{55}}{9}$

Decimal Form:

$x = 0.71291094 \dots, - 0.93513316 \dots$

Solve Using the Quadratic Formula x(9x+2)=6

Related Questions

Support LCMGCF.com by disabling your adblocker.