1. The quadratic equation $x^2+7x+10=0$ is in the form of $a{x}^2+bx+c=0$.

1. What is the value of $a$?

2. What is the value of $b$?

3. What is the value of $c$?

Examine the solution method that has been started below and use it to answer the remaining three parts of question 1.

Original equation
$x^2+7x+10=0$

Step 1 - Subtract 10 from each side.
$x^2+7x=-10$

Step 2 - Multiply each side by 4.
$4x^2+4(7x)=-4(10)$

Step 3 - Rewrite $4x^2$ as $(2x{)}^2$ and $4(7x)$ as $2(7)2x$.
$(2x{)}^2+2(7)(2x)+\mathrm{\_}\mathrm{\_}\mathrm{\_}{\mathrm{\_}}^2=\mathrm{\_}\mathrm{\_}\mathrm{\_}{\mathrm{\_}}^2-4(10)$

Step 4 - $\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$
$(2x+\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}{)}^2=\mathrm{\_}\mathrm{\_}\mathrm{\_}{\mathrm{\_}}^2-4(10)$

Step 5 - $\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$
$2x+\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}=\pm \sqrt{\mathrm{\_}\mathrm{\_}\mathrm{\_}{\mathrm{\_}}^2-4(10)}$

Step 6 - $\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$
$2x=\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\pm \sqrt{\mathrm{\_}\mathrm{\_}\mathrm{\_}{\mathrm{\_}}^2-4(10)}$

Step 7 - $\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$
$x=\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}$

4. In Step 2, what might be a good reason for multiplying each side of the equation by 4?

5. Complete the unfinished steps, then select two solutions.

1. -10
2. -5
3. -2
4. -4

6. Substitute the values of $a$, $b$, and $c$ into the quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, but do not evaluate any of the expressions. Explain how this expression is related to solving $x^2+7x+10=0$ by completing the square.

1. What is the value of $a$?

2. What is the value of $b$?

3. What is the value of $c$?

4. Can you use the quadratic formula to solve this equation?

5. Can you solve this equation using square roots?

3. Clare is deriving the quadratic formula by solving $a{x}^2+bx+c=0$ by completing the square.
   
   She arrived at this equation: $(2ax+b{)}^2=b^2-4ac$.
   
   Choose the best description of what she needs to do to finish solving for $x$.