Given:
The quadratic equation is
[tex]x^2+1=2x-3[/tex]
To find:
The expression that correctly sets up the quadratic formula with the given equation.
Solution:
We have,
[tex]x^2+1=2x-3[/tex]
[tex]x^2+1-2x+3=0[/tex]
[tex]x^2-2x+4=0[/tex]
On comparing with [tex]ax^2+bx+c=0[/tex], we get
[tex]a=1,b=-2,c=4[/tex]
The quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Putting [tex]a=1,b=-2,c=4[/tex], we get
[tex]x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex]
Therefore, the required expression is [tex]\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex].
