Solve for x x=(-6+- square root of 6^2-435)/(2*3)

$x = \frac{- 6 + - \sqrt{6^{2} - 4 \cdot 3 \cdot 5}}{2 \cdot 3}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$x = \frac{- 6 - \sqrt{6^{2} - 4 \cdot 3 \cdot 5}}{2 \cdot 3}$

Step 2

Simplify the numerator.

Raise $6$ to the power of $2$ .

$x = \frac{- 6 - \sqrt{36 - 4 \cdot 3 \cdot 5}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 5$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 6 - \sqrt{36 - 12 \cdot 5}}{2 \cdot 3}$

Multiply $- 12$ by $5$ .

$x = \frac{- 6 - \sqrt{36 - 60}}{2 \cdot 3}$

Subtract $60$ from $36$ .

$x = \frac{- 6 - \sqrt{- 24}}{2 \cdot 3}$

Rewrite $- 24$ as $- 1 (24)$ .

$x = \frac{- 6 - \sqrt{- 1 (24)}}{2 \cdot 3}$

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$x = \frac{- 6 - (\sqrt{- 1} \cdot \sqrt{24})}{2 \cdot 3}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 6 - (i \cdot \sqrt{24})}{2 \cdot 3}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \frac{- 6 - (i \cdot \sqrt{4 (6)})}{2 \cdot 3}$

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

$x = \frac{- 6 - (i \cdot \sqrt{2^{2} \cdot 6})}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 6 - (i \cdot (2 \sqrt{6}))}{2 \cdot 3}$

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

$x = \frac{- 6 - (2 \cdot i \sqrt{6})}{2 \cdot 3}$

Multiply $2$ by $- 1$ .

$x = \frac{- 6 - 2 i \sqrt{6}}{2 \cdot 3}$

Step 3

Simplify terms.

Multiply $2$ by $3$ .

$x = \frac{- 6 - 2 i \sqrt{6}}{6}$

Cancel the common factor of $- 6 - 2 i \sqrt{6}$ and $6$ .

Factor $2$ out of $- 6$ .

$x = \frac{2 (- 3) - 2 i \sqrt{6}}{6}$

Factor $2$ out of $- 2 i \sqrt{6}$ .

$x = \frac{2 (- 3) + 2 (- i \sqrt{6})}{6}$

Factor $2$ out of $2 (- 3) + 2 (- i \sqrt{6})$ .

$x = \frac{2 (- 3 - i \sqrt{6})}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 (- 3 - i \sqrt{6})}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 (- 3 - i \sqrt{6})}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{- 3 - i \sqrt{6}}{3}$

Rewrite $- 3$ as $- 1 (3)$ .

$x = \frac{- 1 (3) - i \sqrt{6}}{3}$

Factor $- 1$ out of $- i \sqrt{6}$ .

$x = \frac{- 1 (3) - (i \sqrt{6})}{3}$

Factor $- 1$ out of $- 1 (3) - (i \sqrt{6})$ .

$x = \frac{- 1 (3 + i \sqrt{6})}{3}$

Move the negative in front of the fraction.

$x = - \frac{3 + i \sqrt{6}}{3}$

Solve for x x=(-6+- square root of 6^2-4*3*5)/(2*3)

Related Questions

Support LCMGCF.com by disabling your adblocker.

Solve for x x=(-6+- square root of 6^2-435)/(2*3)