Answer:
[tex](x+10)^2=80.\text{ Option D is correct.}[/tex]
Explanations:
Given the quadratic equation;
[tex]x^2+20x-17=-3[/tex]
We need to derive an equation that has the same solution. To do that, you will simply write the given equation in vertex form using the completing the square method.
Step 1: Subtract 17 to both sides of the equation:
[tex]\begin{gathered} x^2+20x+17-17=-3-17 \\ x^2+20x=-3-17 \\ x^2+20x=-20 \end{gathered}[/tex]
Step 2: Complete the square of the expression on the left-hand side.
[tex]\begin{gathered} (x^2+20x+(\frac{20}{2})^2)-(\frac{20}{2})^2=-20 \\ (x^2+20x+(10)^2)-10^2=-20 \\ (x+10_{})^2-100=-20 \end{gathered}[/tex]
Step 3: Add 100 to both sides of the equation
[tex]\begin{gathered} (x+10)^2-100+100=-20+100 \\ (x+10)^2=80 \end{gathered}[/tex]
This gives the equation with the same solution as the given equation
