Solve the Quadratic Equation: 5x² - 6x + 1 = 0

Solve the following equation:

$5x^2-6x+1=0$

To solve the quadratic equation $5x^2 - 6x + 1 = 0$, we will use the Quadratic Formula:

The Quadratic Formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Identify the coefficients in the equation:

• $a = 5$
• $b = -6$
• $c = 1$

Step 1: Compute the discriminant $b^2 - 4ac$.

$b^2 - 4ac = (-6)^2 - 4 \times 5 \times 1$

$= 36 - 20$

$= 16$

Step 2: Substitute the values into the Quadratic Formula.

$x = \frac{-(-6) \pm \sqrt{16}}{2 \times 5}$

$= \frac{6 \pm 4}{10}$

Step 3: Calculate the two potential solutions for $x$.

• For $x_1$:

$x_1 = \frac{6 + 4}{10} = \frac{10}{10} = 1$

• For $x_2$:

$x_2 = \frac{6 - 4}{10} = \frac{2}{10} = \frac{1}{5}$

The solutions to the quadratic equation are $x_1 = 1$ and $x_2 = \frac{1}{5}$.

Therefore, after comparing with the provided choices, the correct answer is: $(x_1 = 1, x_2 = \frac{1}{5})$, which matches choice 3.