Question

Please help me I finished the first part i need help with the second one

Answer 1

`(x+10)^2=80.\text{ Option D is correct.}`

Explanations:

Given the quadratic equation;

`x^2+20x-17=-3`

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:

`\begin{gathered} x^2+20x+17-17=-3-17 \\ x^2+20x=-3-17 \\ x^2+20x=-20 \end{gathered}`

Step 2: Complete the square of the expression on the left-hand side.

`\begin{gathered} (x^2+20x+((20)/(2))^2)-((20)/(2))^2=-20 \\ (x^2+20x+(10)^2)-10^2=-20 \\ (x+10_{})^2-100=-20 \end{gathered}`

Step 3: Add 100 to both sides of the equation

`\begin{gathered} (x+10)^2-100+100=-20+100 \\ (x+10)^2=80 \end{gathered}`

This gives the equation with the same solution as the given equation