Question

use the quadratic formula to solve for x.
$5x^2 - 5x = 1$
round your answer to the nearest hundredth.
if there is more than one solution, separate them with commas.
$x = \square$

Explanation:

Step1: Rewrite to standard form

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

Step2: Identify a, b, c

$a=5,\ b=-5,\ c=-1$

Step3: Apply quadratic formula

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

Step4: Substitute values

$$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(5)(-1)}}{2(5)} = \frac{5 \pm \sqrt{25 + 20}}{10} = \frac{5 \pm \sqrt{45}}{10}$$

Step5: Simplify and calculate

$\sqrt{45} \approx 6.708$, so:
$x_1 = \frac{5 + 6.708}{10} = 1.1708 \approx 1.17$
$x_2 = \frac{5 - 6.708}{10} = -0.1708 \approx -0.17$

Answer:

$x = 1.17, -0.17$