Solve the equation using the quadratic formula (when necessary, round results to three significant digits). $13.1 x ^ { 2 } - 39 x = 22.1$
A) 3.46, -1.49
B) 4.46, -1.49
C) 3.46
D) 3.46, -0.487
E) 4.46, -0.487

Question

Quizplus · Accepted Answer

The quadratic formula states that for an equation of the form $ax^2+bx+c=0$, the solutions are given by

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

Comparing this form to $13.1x^2-39x=22.1$, we see that $a=13.1$, $b=-39$, and $c=-22.1$. Substituting these values into the quadratic formula and simplifying,

$$x = \frac{39 \pm \sqrt{39^2-4(13.1)(-22.1)}}{2(13.1)}$$

$$x = \frac{39 \pm \sqrt{1521+1158.04}}{26.2}$$

$$x = \frac{39 \pm \sqrt{2679.04}}{26.2}$$

$$x = \frac{39 \pm 51.75}{26.2}$$

So the solutions are $x = \frac{39+51.75}{26.2} \approx 3.46$ and $x = \frac{39-51.75}{26.2} \approx -0.487$. The best choice is D since it is the only one that includes both of these solutions, rounded to three significant digits.

Solve the Equation Using the Quadratic Formula (When Necessary, Round 13.1x2−39x=22.113.1 x ^ { 2 } - 39 x = 22.113.1x2−39x=22.1

Solve the Equation Using the Quadratic Formula (When Necessary, Round $13.1 x ^ { 2 } - 39 x = 22.1$