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$a \exponential{x}{2} + b x + c = 0 $
Solve for a (complex solution)
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Solve for b (complex solution)
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Solve for a
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Solve for b
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ax^{2}+c=-bx
Subtract bx from both sides. Anything subtracted from zero gives its negation.
ax^{2}=-bx-c
Subtract c from both sides.
x^{2}a=-bx-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-bx-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-bx-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
a=-\frac{bx+c}{x^{2}}
Divide -bx-c by x^{2}.
bx+c=-ax^{2}
Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.
bx=-ax^{2}-c
Subtract c from both sides.
xb=-ax^{2}-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax-\frac{c}{x}
Divide -ax^{2}-c by x.
ax^{2}+c=-bx
Subtract bx from both sides. Anything subtracted from zero gives its negation.
ax^{2}=-bx-c
Subtract c from both sides.
x^{2}a=-bx-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-bx-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-bx-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
a=-\frac{bx+c}{x^{2}}
Divide -bx-c by x^{2}.
bx+c=-ax^{2}
Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.
bx=-ax^{2}-c
Subtract c from both sides.
xb=-ax^{2}-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax-\frac{c}{x}
Divide -ax^{2}-c by x.