Question

use the quadratic formula to solve for x.
$6x^2 - 4x = 1$
round your answer to the nearest hundredth.
if there is more than one solution, separate them with commas.
$x = \square$

Explanation:

Step1: Rewrite in standard form

$6x^2 - 4x - 1 = 0$

Step2: Identify a, b, c

$a=6,\ b=-4,\ c=-1$

Step3: Apply quadratic formula

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

Step4: Substitute values

$$x=\frac{-(-4)\pm\sqrt{(-4)^2-4(6)(-1)}}{2(6)}$$

Step5: Calculate discriminant

$\sqrt{16 + 24}=\sqrt{40}\approx6.3246$

Step6: Compute two solutions

$x_1=\frac{4 + 6.3246}{12}\approx\frac{10.3246}{12}\approx0.86$
$x_2=\frac{4 - 6.3246}{12}\approx\frac{-2.3246}{12}\approx-0.19$

Answer:

$x = 0.86, -0.19$