Let's start by rearranging the given quadratic equation [tex]\( x^2 + 1 = 2x - 3 \)[/tex] into the standard form [tex]\( ax^2 + bx + c = 0 \)[/tex].
1. Start with the given equation:
[tex]\[
x^2 + 1 = 2x - 3
\][/tex]
2. Move all terms to one side to set the equation to [tex]\( 0 \)[/tex]:
[tex]\[
x^2 + 1 - 2x + 3 = 0
\][/tex]
3. Simplify the equation:
[tex]\[
x^2 - 2x + 4 = 0
\][/tex]
Now that the equation is in the standard quadratic form [tex]\( ax^2 + bx + c = 0 \)[/tex], we can identify the coefficients:
[tex]\[
a = 1, \quad b = -2, \quad c = 4
\][/tex]
Next, we use the quadratic formula to find the roots of the equation:
[tex]\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\][/tex]
Substituting the coefficients [tex]\( a = 1 \)[/tex], [tex]\( b = -2 \)[/tex], and [tex]\( c = 4 \)[/tex] into the quadratic formula, we get:
[tex]\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(4)}}{2(1)}
\][/tex]
Therefore, the correct expression is:
[tex]\[
\frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(4)}}{2(1)}
\][/tex]
This matches option A. The correct setup for the quadratic formula is:
A. [tex]\(\frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(4)}}{2(1)}\)[/tex]
