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

Question

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

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The final solution of the quadratic equation is

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

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