Solve Using the Quadratic Formula 5x^2-10x+5=0

$5 x^{2} - 10 x + 5 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 5$ , $b = - 10$ , and $c = 5$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $5$ .

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

Multiply $- 20$ by $5$ .

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

Subtract $100$ from $100$ .

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

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

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

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

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

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

$x = \frac{10}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{10}{10}$

Divide $10$ by $10$ .

$x = 1$

Step 4

The final answer is the combination of both solutions.

$x = 1$ Double roots