Question

homework assignment 2.5 quadratic equations due friday by 11:59pm points 15 submitting an external tool homework assignment 2.5 quadratic equations score: 10/15 answered: 10/15 question 11 solve the equation: 20x^2 = x + 1. fully simplify your answer, including any non - real solutions. x = question help: video written example

Explanation:

Step1: Rearrange to standard form

Move all terms to one - side: $20x^{2}-x - 1=0$.

Step2: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, here $a = 20$, $b=-1$, $c = - 1$.

Step3: Use quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $x=\frac{-(-1)\pm\sqrt{(-1)^{2}-4\times20\times(-1)}}{2\times20}=\frac{1\pm\sqrt{1 + 80}}{40}=\frac{1\pm\sqrt{81}}{40}$.

Step4: Simplify the solutions

Since $\sqrt{81}=9$, we have $x=\frac{1\pm9}{40}$. So $x_1=\frac{1 + 9}{40}=\frac{10}{40}=\frac{1}{4}$ and $x_2=\frac{1-9}{40}=\frac{-8}{40}=-\frac{1}{5}$.

Answer:

$x=\frac{1}{4},-\frac{1}{5}$