Write the quadratic equation in general form. Do not solve the equation.
x(x + 3) = 4x^2 + 4
just expand it
x^2 + 3x = 4x^2 + 4
0 = 3x^2 - 3x + 4
or
3x^2 - 3x + 4 = 0
What part of this did you find difficult?
To write a quadratic equation in general form, we gather like terms and set the equation equal to zero. Let's start by simplifying the right side of the equation:
4x^2 + 4
Since x(x + 3) is already simplified, we can rewrite the equation as:
x(x + 3) - (4x^2 + 4) = 0
Now, let's distribute the x to simplify further:
x^2 + 3x - (4x^2 + 4) = 0
Next, let's distribute the negative sign across the terms in parentheses:
x^2 + 3x - 4x^2 - 4 = 0
Now, combine like terms:
-3x^2 + 3x - 4 = 0
We have now written the quadratic equation in general form:
-3x^2 + 3x - 4 = 0