Question

Complete the steps of the derivation of the quadratic formula step 1: (x+b/2a)^2-b^2-4ac/4a^2=0

Answer 1

The final solution of the quadratic equation is

`x=(-b\pm√(b^2-4ac))/(2a)`

Explanation:

Given : The steps of the derivation of the quadratic formula

Step 1:
`(x+(b)/(2a))^2-(b^2-4ac)/(4a^2)=0`

To find : Complete the steps.

Solution :

Step 1: Write the expression

`(x+(b)/(2a))^2-(b^2-4ac)/(4a^2)=0`

Step 2: Re-write the expression

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

Step 3 : Square Root both side

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

Step 4: Simplifying we get

`x+(b)/(2a)=(√(b^2-4ac))/(2a)`

Step 5: Make x the subject

`x=(√(b^2-4ac))/(2a)-(b)/(2a)`

Therefore, The final solution of the quadratic equation is

`x=(-b\pm√(b^2-4ac))/(2a)`

Answer 2

(x+b/2a)^2-(b^2-4ac)/2a=0
Step 2:
Re-write the expression:
(x+b/2a)^2=(b^2-4ac)/4a^2

Step 3:
get the square root of both sides:
x+b/2a=sqrt[(b^2-4ac)/4a^2]

Step 4:
Simplifying we get:
x+b/2a=sqrt[b^2-4ac]/2a

Step 5
Make x the subject:
x=-b/2a+/-sqrt[b^2-4ac]/2a