Answer:
Step-by-step explanation:
perfect sqaure formula (u+w)²=u²+2uw+w²
ax²+bx+c=0 divide by a
[tex]x^{2} +\frac{bx}{a} + \frac{c}{a} =0[/tex] so u=1, 2uw=2*1*w= b/a, so w=b/2a
[tex](x^{2}+ \frac{bx}{a} +\frac{b^{2} }{4a^{2} } ) +\frac{c}{a} -\frac{b^{2} }{4a^{2} }=0[/tex] now that we formed the perfect sqare solve
[tex](x +\frac{b}{2a} )^{2} +\frac{c*4*a-b^{2} }{4a^{2} } =0[/tex] but we can factor a negative in front of the fraction
[tex](x+\frac{b}{2a} )^{2} -\frac{b^{2} -4ac }{4a^{2} } =0[/tex] now isolate the 2 terms and squareroot both sides
[tex]\sqrt{ (x +\frac{b}{2a} )^{2}} =\sqrt{ \frac{b^{2} -4ac }{4a^{2} } }[/tex] and you will be left with
[tex]x +\frac{b}{2a} =\ + - \frac {\sqrt{ b^{2} -4ac} }{2a }[/tex] subtract b/2a from both sides
x= [tex]\frac{-b+ - \sqrt{b^{2}-4ac } }{2a}[/tex]
