Solve Using the Quadratic Formula 5u(u+2)+5=0

$5 u (u + 2) + 5 = 0$

Step 1

Simplify the left side.

Simplify each term.

Apply the distributive property.

$5 u \cdot u + 5 u \cdot 2 + 5 = 0$

Multiply $u$ by $u$ by adding the exponents.

Move $u$ .

$5 (u \cdot u) + 5 u \cdot 2 + 5 = 0$

Multiply $u$ by $u$ .

$5 u^{2} + 5 u \cdot 2 + 5 = 0$

Multiply $2$ by $5$ .

$5 u^{2} + 10 u + 5 = 0$

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 $a = 5$ , $b = 10$ , and $c = 5$ into the quadratic formula and solve for $u$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (5 \cdot 5)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

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

$u = \frac{- 10 \pm \sqrt{100 - 4 \cdot 5 \cdot 5}}{2 \cdot 5}$

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

Multiply $- 4$ by $5$ .

$u = \frac{- 10 \pm \sqrt{100 - 20 \cdot 5}}{2 \cdot 5}$

Multiply $- 20$ by $5$ .

$u = \frac{- 10 \pm \sqrt{100 - 100}}{2 \cdot 5}$

Subtract $100$ from $100$ .

$u = \frac{- 10 \pm \sqrt{0}}{2 \cdot 5}$

Rewrite $0$ as $0^{2}$ .

$u = \frac{- 10 \pm \sqrt{0^{2}}}{2 \cdot 5}$

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

$u = \frac{- 10 \pm 0}{2 \cdot 5}$

$- 10$ plus or minus $0$ is $- 10$ .

$u = \frac{- 10}{2 \cdot 5}$

Multiply $2$ by $5$ .

$u = \frac{- 10}{10}$

Divide $- 10$ by $10$ .

$u = - 1$

Step 5

The final answer is the combination of both solutions.

$u = - 1$ Double roots