Question

The first two steps in the derivation of the quadratic formula by completing the square are shown below.

Which answer choice shows the correct next step?
Step 1: ax^2+ bx+c = 0
Step 2: ax^2 + bx=-c

Answer 1

C on edge

Explanation:

Answer 2

The correct next step is the answer choice

`x^(2) +(b)/(a)x=-(c)/(a)`

Explanation:

we have the quadratic equation in standard form

`ax^(2)+bx+c=0`

The steps in the derivation of the quadratic formula by completing the square are

step 1

`ax^(2)+bx+c=0` ----> given equation

step 2

Move the constant term over to the right-hand side

`ax^(2)+bx=-c`

step 3

The leading term is multiplied by a

so

Divide by a both sides

`x^(2) +(b)/(a)x=-(c)/(a)`

step 4

Multiply the linear term by 1/2

`(b)/(a)((1)/(2))=+(b)/(2a)`

step 5

square this derived value

`+(b^2)/(4a^2)`

step 6

Add this squared value to either side of the equation

`x^(2) +(b)/(a)x+(b^2)/(4a^2)=-(c)/(a)+(b^2)/(4a^2)`

step 7

convert to the common denominator, and combine on the right-hand side

`x^(2) +(b)/(a)x+(b^2)/(4a^2)=(b^2-4ac)/(4a^2)`

step 8

convert the left-hand side to completed-square form

`(x+(b)/(2a))^(2)=(b^2-4ac)/(4a^2)`

step 9

take the square roots of either side

`(x+(b)/(2a))=(+/-)\sqrt{(b^2-4ac)/(4a^2)} \\\\(x+(b)/(2a))=(+/-)(√(b^2-4ac))/(2a)`

step 10

solving for the variable

`x=-(b)/(2a)(+/-)(√(b^2-4ac))/(2a)\\\\x=(-b(+/-)√(b^2-4ac))/(2a)`