Proving Quadratic FormulaHow does \frac{b}{2a} become b^{2}}{4a^{2}}?

logosomatw 2022-01-23 Answered

Proving Quadratic Formula
How does b2a become b24a2?

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Expert Answer

bemolizisqt
Answered 2022-01-24 Author has 16 answers
Step 1
Remember how to complete the square:
Ax2+Bx=A(x+B2A)2B24A2
So now
ax2+bx+c=0 complete square
a(x+b2a)2b24a=c
(x+b2a)2=b24ac4a2
x1, 2+b2a=±b24ac2a
x1, 2=b±b24ac2a
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RizerMix
Answered 2022-01-27 Author has 438 answers

Step 1
ax2+bx+c=0 divide by a because a0
we get
x2+bax+ca=0
x2+2xb2a+ca=0
x2+2xb2a+b24a2b24a2+ca=0
x2+2xb2a+b24a2=b24a2ca
x2+2xb2a+b24a2=b24ac4a2
x2+2xb2a+(b2a)2=b24ac4a2
if in LHS we use x=A and b2a=B then we have
A2+2AB+B2=(A+B)2
or
(x+b2a)2=b24ac4a2
we have two values of square roote
x1+b2a=+b24ac4a2
and
x2+b2a=b24ac4a2
or
x1, 2=b±b24ac2a

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nick1337
Answered 2022-01-27 Author has 510 answers
Step 1 ax2+bx+c=0 ax2+bx=c x2+bax=ca x2+2x(b2a)+(b2a)2(b2a)2=ca (x+b2a)2b24a2=ca (x+b2a)2=b24ac4a2 x+b2a=±b24ac2a x=b±b24ac2a
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