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

(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

Answer 2

Answer:

The final solution of the quadratic equation is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step-by-step explanation:

Given : The steps of the derivation of the quadratic formula

Step 1: $(x+\frac{b}{2a})^2-\frac{b^2-4ac}{4a^2}=0$

To find : Complete the steps.

Solution :

Step 1: Write the expression

$(x+\frac{b}{2a})^2-\frac{b^2-4ac}{4a^2}=0$

Step 2:  Re-write the expression  

$(x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}$

Step 3 : Square Root both side

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

Step 4:  Simplifying we get

$x+\frac{b}{2a}=\frac{\sqrt{b^2-4ac}}{2a}$

Step 5:  Make x the subject

$x=\frac{\sqrt{b^2-4ac}}{2a}-\frac{b}{2a}$

Therefore, The final solution of the quadratic equation is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$