Solve for x x=(-10+- square root of 10^2-456)/(2*5)

$x = \frac{- 10 + - \sqrt{10^{2} - 4 \cdot 5 \cdot 6}}{2 \cdot 5}$

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 $1 \cdot - 1 = - 1$

$x = \frac{- 10 - \sqrt{10^{2} - 4 \cdot 5 \cdot 6}}{2 \cdot 5}$

Simplify the numerator.

Raise $10$ to the power of $2$ .

$x = \frac{- 10 - \sqrt{100 - 4 \cdot 5 \cdot 6}}{2 \cdot 5}$

Multiply $- 4$ by $5$ .

$x = \frac{- 10 - \sqrt{100 - 20 \cdot 6}}{2 \cdot 5}$

Multiply $- 20$ by $6$ .

$x = \frac{- 10 - \sqrt{100 - 120}}{2 \cdot 5}$

Subtract $120$ from $100$ .

$x = \frac{- 10 - \sqrt{- 20}}{2 \cdot 5}$

Rewrite $- 20$ as $- 1 (20)$ .

$x = \frac{- 10 - \sqrt{- 1 (20)}}{2 \cdot 5}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$x = \frac{- 10 - (\sqrt{- 1} \cdot \sqrt{20})}{2 \cdot 5}$

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

$x = \frac{- 10 - (i \cdot \sqrt{20})}{2 \cdot 5}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x = \frac{- 10 - (i \cdot \sqrt{4 (5)})}{2 \cdot 5}$

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

$x = \frac{- 10 - (i \cdot \sqrt{2^{2} \cdot 5})}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{- 10 - (i \cdot (2 \sqrt{5}))}{2 \cdot 5}$

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

$x = \frac{- 10 - (2 \cdot i \sqrt{5})}{2 \cdot 5}$

Multiply $2$ by $- 1$ .

$x = \frac{- 10 - 2 i \sqrt{5}}{2 \cdot 5}$

Simplify terms.

Multiply $2$ by $5$ .

$x = \frac{- 10 - 2 i \sqrt{5}}{10}$

Cancel the common factor of $- 10 - 2 i \sqrt{5}$ and $10$ .

Factor $2$ out of $- 10$ .

$x = \frac{2 (- 5) - 2 i \sqrt{5}}{10}$

Factor $2$ out of $- 2 i \sqrt{5}$ .

$x = \frac{2 (- 5) + 2 (- i \sqrt{5})}{10}$

Factor $2$ out of $2 (- 5) + 2 (- i \sqrt{5})$ .

$x = \frac{2 (- 5 - i \sqrt{5})}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$x = \frac{2 (- 5 - i \sqrt{5})}{2 \cdot 5}$

Cancel the common factor.

$x = \frac{2 (- 5 - i \sqrt{5})}{2 \cdot 5}$

Rewrite the expression.

$x = \frac{- 5 - i \sqrt{5}}{5}$

Rewrite $- 5$ as $- 1 (5)$ .

$x = \frac{- 1 (5) - i \sqrt{5}}{5}$

Factor $- 1$ out of $- i \sqrt{5}$ .

$x = \frac{- 1 (5) - (i \sqrt{5})}{5}$

Factor $- 1$ out of $- 1 (5) - (i \sqrt{5})$ .

$x = \frac{- 1 (5 + i \sqrt{5})}{5}$

Move the negative in front of the fraction.

$x = - \frac{5 + i \sqrt{5}}{5}$

Solve for x x=(-10+- square root of 10^2-4*5*6)/(2*5)

Related Questions

Support LCMGCF.com by disabling your adblocker.

Solve for x x=(-10+- square root of 10^2-456)/(2*5)