Question

Consider the first five steps of the derivation of the Quadratic Formula.

ax²+bx+c=0
x²+²x+²=0
x²+²x+=+
What is the next step?

Answer 1

Full proof below

Explanation:

`\displaystyle ax^2+bx+c=0\\\\ax^2+bx=-c\\\\x^2+\biggr((b)/(a)\biggr)x=-(c)/(a)\\\\x^2+\biggr((b)/(a)\biggr)x+\biggr((b)/(2a)\biggr)^2=-(c)/(a)+\biggr((b)/(2a)\biggr)^2\\\\x^2+\biggr((b)/(a)\biggr)x+(b^2)/(4a^2)=-(c)/(a)+(b^2)/(4a^2)\\ \\\biggr(x+(b)/(2a)\biggr)^2=-(4ac)/(4a^2)+(b^2)/(4a^2)\\ \\\biggr(x+(b)/(2a)\biggr)^2=(b^2-4ac)/(4a^2)\\ \\x+(b)/(2a)=\pm(√(b^2-4ac))/(2a)\\ \\x=(-b\pm√(b^2-4ac))/(2a)`