Question

Factor and SOLVE the following quadratic, 3x^2 + 13x = -4, and select all solutions that apply.-1 4121/3-1/3-4

Answer 1

the equation given

we can rewrite the equation as

`3x^2+13+4=0`

to solve this question, we can use any of the given mehod known to solve quadratic equations which are

1. factorization

2. completing the squares

3. using quadratic equation

for the purpose of this tutoring session, i'll use quadratic equation also know as quadractic formula

the formula is given as

`x=-b\pm\frac{\sqrt[]{b^2-4ac}}{2a}`

next we proceed to identify the variables

`\begin{gathered} 3x^2+13x+4 \\ a=3 \\ b=13 \\ c=4 \end{gathered}`

now we can input the values into the equation (formula) above

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-13\pm\sqrt[]{13^2-4(3)(4)}}{2(3)} \\ x=\frac{-13\pm\sqrt[]{169-48}}{6} \\ x=\frac{-13\pm\sqrt[]{121}}{6} \\ x=(-13\pm11)/(6) \\ x=-(13+11)/(6) \\ or \\ x=-(13-11)/(6) \\ x=-(2)/(6) \\ or \\ x=-(24)/(6) \\ x=-(1)/(3) \\ or \\ x=-4 \end{gathered}`

from the calculations above, x = -1/3 or x = -4