Question

homework assignment 2.5 quadratic equations
due friday by 11:59am points 15 submitting an external tool
homework assignment 2.5 quadratic equations
score: 10/15 answered: 10/15
question 11
solve the equation: 20x² = x + 1. fully simplify your answer, including any non - real solutions.

Explanation:

Step1: Rearrange to standard form

Rearrange $20x^{2}=x + 1$ to $20x^{2}-x - 1=0$.

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 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:

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