SOLUTION: Solve for the value of x of arctan(3 + 4x = x^2) = -pi/4 please if you can help me solve this I have no idea what to do. our prof only ever gives us examples like y = sin (-1/2)

Question 609539: Solve for the value of x of arctan(3 + 4x = x^2) = -pi/4
please if you can help me solve this I have no idea what to do. our prof only ever gives us examples like y = sin (-1/2) and honestly I don't know what to do with whatever information I can squeeze out of that simple example to solve something as complicated as this homework.
If you can also explain the steps that'd be really great. Thank you to anyone who answers this.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I assume that the equation is
arctan() =

arctan(something) represents "an angle whose tan ratio is 'something'". So
arctan()
represents an angle whose tan ratio is ).
And the equation
arctan() =
tells us that this angle is
We should know that . Since and since the equation arctan() = tells us that the tan of the same angle is also then and -1 must be equal to each other. Now we just have to solve:

Since this is a quadratic equation we want one side to be zero. Adding 1 to each side we get:

Next we factor (or use the Quadratic Formula). To make the factoring easier, I'm going to rearrange the terms:

This factors easily into:
(x+2)(x+2) = 0
From the Zero Product Property we know that one or more of the factors must be zero. So
x + 2 = 0
Solving we get
x = -2
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