An equation of the form
\n\\[ax^2+bx+c=0\\text{,}\\]
\n\ncan be solved using the quadratic formula
\n\\[x={\\frac {-b\\pm\\sqrt{b^2-4\\times a\\times c}}{2a}}\\text{.}\\]
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$\\simplify{{a1}x^2+{a2}x+{a3}={a4}}$
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$\\simplify{{b1}x^2+{b2}x+{b3}={b4}x}$
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"}, "advice": "The quadratic formula is
\n\\[x={\\frac {-b\\pm\\sqrt{b^2-4\\times a\\times c}}{2a}}\\text{.}\\]
\nFrom the equation, we can read off values for $a$, $b$ and $c$:
\n\\[\\begin{align}
a&=1\\text{,}\\\\
b&=\\var{a+m}\\text{,}\\\\
c&=\\var{a*m} \\text{.}
\\end{align}\\]
Substituting these values into the quadratic formula,
\n\\[x = \\frac {-\\var{a+m}\\pm\\sqrt{\\var{a+m}^2-4\\times \\var{a*m}}}{2}\\text{.}\\]
\nNote the $\\pm$ symbol in the formula. This means there are two solutions: one using $+$, the other using $-$.
\nThe two solutions are
\n\\[\\begin{align}
x_1&=\\var{m}\\text{,}\\\\
x_2&=\\var{a}\\text{.}
\\end{align}\\]
Note that the right-hand side of the given equation is not zero. We need to rewrite it in the form $ax^2+bx+c=0$:
\n\\[\\begin{align}
\\simplify{{a1}x^2+{a2}x+{a3}}&=\\var{a4}\\\\
\\simplify{{a1}x^2+{a2}x+{a3-a4}}&=0\\text{.}
\\end{align}\\]
Then we can read off values for $a$, $b$ and $c$:
\n\\[\\begin{align}
a&=\\var{a1}\\\\
b&=\\var{a2}\\\\
c&=\\var{a3-a4} \\text{.}
\\end{align}\\]
We can now substitute these values into the quadratic formula:
\n\\[x = {\\frac {-\\var{a2}\\pm\\sqrt{\\var{a2}^2-4\\times \\var{a1}\\times \\var{a3-a4}}}{2\\times\\var{a1}}}\\text{.}\\]
\nSo the two solutions are
\n\\[\\begin{align}
x_1&=\\var{dpformat(x1,2)}\\\\
x_2&=\\var{dpformat(x2,2)}\\text{.}
\\end{align}\\]
We first rearrange our equation into the form $ax^2+bx+c=0$:
\n\\[\\begin{align}
\\simplify{{b1}x^2+{b2}x+{b3}}&=0=\\var{b4}x\\\\
\\simplify{{b1}x^2+{b2-b4}x+{b3}}&=0\\text{.}
\\end{align}\\]
We can then read off the values for $a, b$ and $c$, which are
\n\\[\\begin{align}
a&=\\var{b1}\\text{,}\\\\
b&=\\var{b2-b4}\\text{,}\\\\
c&=\\var{b3}\\text{.}
\\end{align}\\]
Substituting these values into the quadratic formula,
\n\\[x = {\\frac {-\\var{b2-b4}\\pm\\sqrt{\\var{b2-b4}^2-4\\times \\var{b1}\\times \\var{b3}}}{2\\times\\var{b1}}},\\]
\nwe obtain solutions
\n\\[\\begin{align}
x_1&=\\var{dpformat(p1,2)}\\text{,}\\\\
x_2&=\\var{dpformat(p2,2)}\\text{.}
\\end{align}\\]