using the quadratic formula to solve 11x² - 4x = 1, what are the values of x?\n$\frac{2}{11}pm\frac{sqrt{15}}…

using the quadratic formula to solve 11x² - 4x = 1, what are the values of x?\n$\frac{2}{11}pm\frac{sqrt{15}}{11}$\n$\frac{2}{11}pm\frac{2sqrt{15}}{11}$\n$\frac{2}{11}pm\frac{sqrt{7}}{11}$\n$\frac{2}{11}pm\frac{sqrt{7}i}{11}$

using the quadratic formula to solve 11x² - 4x = 1, what are the values of x?\n$\frac{2}{11}pm\frac{sqrt{15}}{11}$\n$\frac{2}{11}pm\frac{2sqrt{15}}{11}$\n$\frac{2}{11}pm\frac{sqrt{7}}{11}$\n$\frac{2}{11}pm\frac{sqrt{7}i}{11}$

Answer

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $11x^{2}-4x = 1$ as $11x^{2}-4x - 1=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 11$, $b=-4$, $c=-1$.

Step2: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 11$, $b=-4$, $c=-1$ into it. First calculate the discriminant $\Delta=b^{2}-4ac=(-4)^{2}-4\times11\times(-1)=16 + 44=60$. Then $x=\frac{-(-4)\pm\sqrt{60}}{2\times11}=\frac{4\pm2\sqrt{15}}{22}=\frac{2\pm\sqrt{15}}{11}$.

Answer:

$\frac{2}{11}\pm\frac{\sqrt{15}}{11}$