Answer:
Yes, see the explanation.
Roots:
x = [tex]\frac{63}{8}[/tex], or x= -10
Step-by-step explanation:
A quadratic fomrual in standard form is;
ax^(2) + bx + c = 0
The given equation:
4x^2 = -9x - 4
Maniplate the equation using inverse operations
4x^2 = -9x - 4
-4x^2 -4x^2
0 = -4x^2 - 9x - 4
Yes, this is a quadratic equation, because it fits the requirement of being able to be written in standard form.
Now find its roots:
-4x^2 -9x - 4 = 0
remember,
x = [tex]\frac{(-b) +- (\sqrt{b^{2} - 4ac }) }{2a}[/tex]
Substitute in the given values
x= [tex]\frac{(-(-9)) +- (\sqrt{(-9)^{2} - 4(-4)(-4)}) }{2(-4)}[/tex]
Simplify,
x = [tex]\frac{9 +- (\sqrt{5184}) }{-8}[/tex]
x = [tex]\frac{9 +- 72}{-8}[/tex]
x = [tex]\frac{63}{8}[/tex]
or
x= -10
