Explanation
We are given the following:
[tex]x=\frac{-(-5)\pm\sqrt{(-5)^2-4(7)(-2)}}{2(7)}[/tex]
We are required to determine the equation Michelle solved.
We know that a quadratic equation in its general form can be solved thus:
Therefore, we can deduce from the details given that:
[tex]\begin{gathered} b=-5 \\ a=7 \\ c=-2 \\ The\text{ }equation\text{ }should\text{ }be:7x^2-5x-2=0 \end{gathered}[/tex]
Simplifying the options, we have:
[tex]\begin{gathered} Option\text{ }A:7x^2-5x+3=5 \\ 7x^2-5x+3-5=0 \\ 7x^2-5x-2=0 \\ \\ Option\text{ }B:7x^2-5x-2=-1 \\ 7x^2-5x-2+1=0 \\ 7x^2-5x-1=0 \\ \\ Option\text{ }C:7x^2-5x+6=-8 \\ 7x^2-5x+6+8=0 \\ 7x^2-5x+14=0 \\ \\ Option\text{ }D:7x^2-5x+5=3 \\ 7x^2-5x+5-3=0 \\ 7x^2-5x+2=0 \end{gathered}[/tex]
Hence, the answer is:
[tex]7x^2-5x+3=5[/tex]
The first option is correct.
