Which of the following equations are equivalent to
a
x
2
+
b
x
+
c
=
0
\displaystyle {a}{x}^{{2}}+{b}{x}+{c}={0}
a
x
2
+
b
x
+
c
=
0
?
x
=
−
b
±
b
2
−
4
a
c
2
a
\displaystyle {x}=-{b}\pm\frac{\sqrt{{{b}^{{2}}-{4}{a}{c}}}}{{{2}{a}}}
x
=
−
b
±
2
a
b
2
−
4
a
c
x
2
+
b
a
x
+
c
a
=
0
\displaystyle {x}^{{2}}+\frac{{b}}{{a}}{x}+\frac{{c}}{{a}}={0}
x
2
+
a
b
x
+
a
c
=
0
(
x
+
b
2
a
)
2
=
b
2
−
4
a
c
2
a
\displaystyle {\left({x}+\frac{{b}}{{{2}{a}}}\right)}^{{2}}=\frac{{{b}^{{2}}-{4}{a}{c}}}{{{2}{a}}}
(
x
+
2
a
b
)
2
=
2
a
b
2
−
4
a
c
x
2
+
b
x
=
−
c
\displaystyle {x}^{{2}}+{b}{x}=-{c}
x
2
+
b
x
=
−
c
x
=
−
b
±
b
2
−
4
a
c
2
a
\displaystyle {x}=\frac{{-{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}
x
=
2
a
−
b
±
b
2
−
4
a
c
(
x
+
b
2
a
)
2
=
b
2
−
4
a
c
4
a
2
\displaystyle {\left({x}+\frac{{b}}{{{2}{a}}}\right)}^{{2}}=\frac{{{b}^{{2}}-{4}{a}{c}}}{{{4}{a}^{{2}}}}
(
x
+
2
a
b
)
2
=
4
a
2
b
2
−
4
a
c
a
x
2
+
b
x
=
−
c
\displaystyle {a}{x}^{{2}}+{b}{x}=-{c}
a
x
2
+
b
x
=
−
c
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