Question

1. solve using the quadratic formula: 2x² + 3x = 20. in chemistry, any negative answers are not relevant (and not included) since molarity and other such quantities cannot be negative.

Explanation:

Step1: Rewrite the equation in standard quadratic form

First, rewrite $2x^{2}+3x = 20$ as $2x^{2}+3x - 20=0$. Here, $a = 2$, $b = 3$, and $c=- 20$.

Step2: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 2$, $b = 3$, and $c=-20$ into it. Calculate $b^{2}-4ac=(3)^{2}-4\times2\times(-20)=9 + 160 = 169$.

Step3: Find the values of x

$x=\frac{-3\pm\sqrt{169}}{2\times2}=\frac{-3\pm13}{4}$.
Case 1: When we take the plus - sign, $x=\frac{-3 + 13}{4}=\frac{10}{4}=\frac{5}{2}$.
Case 2: When we take the minus - sign, $x=\frac{-3-13}{4}=\frac{-16}{4}=-4$. But since in chemistry negative values for relevant quantities (as mentioned in the problem) are not valid, we discard $x=-4$.

Answer:

$x=\frac{5}{2}$