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

(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 Link

tardymanchester tardymanchester · Answer 2 · 2019-04-22T06:46:09+02:00

Answer:

The final solution of the quadratic equation is

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Step-by-step explanation:

Given : The steps of the derivation of the quadratic formula

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

To find : Complete the steps.

Solution :

Step 1: Write the expression

[tex](x+\frac{b}{2a})^2-\frac{b^2-4ac}{4a^2}=0[/tex]

Step 2: Re-write the expression

[tex](x+\frac{b}{2a})^2=\frac{b^2-4ac}{4a^2}[/tex]

Step 3 : Square Root both side

[tex](x+\frac{b}{2a})=\sqrt{\frac{b^2-4ac}{4a^2}}[/tex]

Step 4: Simplifying we get

[tex]x+\frac{b}{2a}=\frac{\sqrt{b^2-4ac}}{2a}[/tex]

Step 5: Make x the subject

[tex]x=\frac{\sqrt{b^2-4ac}}{2a}-\frac{b}{2a}[/tex]

Therefore, The final solution of the quadratic equation is

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]