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Basic Math
Arithmetic
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Example
3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b
Question
$${ x }^{ 2 } +8x+74=0$$
Answer
x=-4+sqrt(58)*IM,-4-sqrt(58)*IM
Solution
Use the Quadratic Formula.
In general, given \(a{x}^{2}+bx+c=0\), there exists two solutions where:
\[x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}\]
In this case, \(a=1\), \(b=8\) and \(c=74\).
\[{x}^{}=\frac{-8+\sqrt{{8}^{2}-4\times 74}}{2},\frac{-8-\sqrt{{8}^{2}-4\times 74}}{2}\]
Simplify.
\[x=\frac{-8+2\sqrt{58}\imath }{2},\frac{-8-2\sqrt{58}\imath }{2}\]
\[x=\frac{-8+2\sqrt{58}\imath }{2},\frac{-8-2\sqrt{58}\imath }{2}\]
Simplify solutions.
\[x=-4+\sqrt{58}\imath ,-4-\sqrt{58}\imath \]
x=-4+sqrt(58)*IM,-4-sqrt(58)*IM
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