Solve Using the Quadratic Formula 5x^2+1/5=2x

$5 x^{2} + \frac{1}{5} = 2 x$

Step 1

Subtract $2 x$ from both sides of the equation.

$5 x^{2} + \frac{1}{5} - 2 x = 0$

Step 2

Multiply through by the least common denominator $5$ , then simplify.

Apply the distributive property.

$5 (5 x^{2}) + 5 (\frac{1}{5}) + 5 (- 2 x) = 0$

Simplify.

Multiply $5$ by $5$ .

$25 x^{2} + 5 (\frac{1}{5}) + 5 (- 2 x) = 0$

Cancel the common factor of $5$ .

Cancel the common factor.

$25 x^{2} + 5 (\frac{1}{5}) + 5 (- 2 x) = 0$

Rewrite the expression.

$25 x^{2} + 1 + 5 (- 2 x) = 0$

Multiply $- 2$ by $5$ .

$25 x^{2} + 1 - 10 x = 0$

Move $1$ .

$25 x^{2} - 10 x + 1 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 25$ , $b = - 10$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (25 \cdot 1)}}{2 \cdot 25}$

Step 5

Simplify.

Simplify the numerator.

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

$x = \frac{10 \pm \sqrt{100 - 4 \cdot 25 \cdot 1}}{2 \cdot 25}$

Multiply $- 4 \cdot 25 \cdot 1$ .

Multiply $- 4$ by $25$ .

$x = \frac{10 \pm \sqrt{100 - 100 \cdot 1}}{2 \cdot 25}$

Multiply $- 100$ by $1$ .

$x = \frac{10 \pm \sqrt{100 - 100}}{2 \cdot 25}$

Subtract $100$ from $100$ .

$x = \frac{10 \pm \sqrt{0}}{2 \cdot 25}$

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

$x = \frac{10 \pm \sqrt{0^{2}}}{2 \cdot 25}$

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

$x = \frac{10 \pm 0}{2 \cdot 25}$

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

$x = \frac{10}{2 \cdot 25}$

Multiply $2$ by $25$ .

$x = \frac{10}{50}$

Cancel the common factor of $10$ and $50$ .

Factor $10$ out of $10$ .

$x = \frac{10 (1)}{50}$

Cancel the common factors.

Factor $10$ out of $50$ .

$x = \frac{10 \cdot 1}{10 \cdot 5}$

Cancel the common factor.

$x = \frac{10 \cdot 1}{10 \cdot 5}$

Rewrite the expression.

$x = \frac{1}{5}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{1}{5}$ Double roots

Solve Using the Quadratic Formula 5x^2+1/5=2x

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