Question

43. Which of the following are solutions to the equation -11x = 2x^2 + 15? Select all that apply. A. -5B. -3C. -5/2D. 5/2E. 3F. 5

Answer 1

We have the next equation

$-11x=2x^2+15$

First we need o make the equation equal to zero

$2x^2+11x+15=0$

we have a quadratic equation,we will have 2 solutions, so we will use the general formula to find the solutions to this equation

$x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

in our case

a=2

b=11

c=15

$x_{1,2}=\frac{-11\pm\sqrt[]{11^2-4(15)(2)}}{2(2)}_{}$$x_{1,2}=\frac{-11\pm\sqrt[]{121-120}}{4}=\frac{-11\pm1}{4}$

for the first solution

$x=\frac{-11+1}{4}=-\frac{10}{4}=-\frac{5}{2}$

for the second solution

$x=\frac{-11-1}{4}=\frac{-12}{4}=-3$

the solutions to the equation given is

$x=-\frac{5}{2},\: x=-3$

the correct choices are B. and C.