To determine the standard form of the given equation [tex]\( x^2 - 3 = 2x - 4x^2 + 6 \)[/tex], we need to rearrange all terms so that we have a single quadratic expression set equal to zero.
Here is the step-by-step process:
1. Write down the original equation:
[tex]\[
x^2 - 3 = 2x - 4x^2 + 6
\][/tex]
2. Move all terms to the left side to set the equation to zero:
[tex]\[
x^2 - 3 - 2x + 4x^2 - 6 = 0
\][/tex]
3. Combine the like terms on the left side:
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[
x^2 + 4x^2 = 5x^2
\][/tex]
- Combine the linear terms:
[tex]\[
-2x
\][/tex]
- Combine the constant terms:
[tex]\[
-3 - 6 = -9
\][/tex]
Putting these together, we get:
[tex]\[
5x^2 - 2x - 9 = 0
\][/tex]
Thus, the standard form of the equation [tex]\( x^2 - 3 = 2x - 4x^2 + 6 \)[/tex] is:
[tex]\[
\boxed{5x^2 - 2x - 9 = 0}
\][/tex]
So, the correct answer is:
[tex]\[
5x^2 - 2x - 9 = 0
\][/tex]
