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Example
3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b
Question
$$4x^{2}+2\cdot=18+35x$$
Answer
x=(35+sqrt(1801))/8,(35-sqrt(1801))/8
Solution
Move all terms to one side.
\[4{x}^{2}+2\times -18-35x=0\]
Simplify \(2\times -18\) to \(-36\).
\[4{x}^{2}-36-35x=0\]
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, \(a=4\), \(b=-35\) and \(c=-36\).
\[{x}^{}=\frac{35+\sqrt{{(-35)}^{2}-4\times 4\times -36}}{2\times 4},\frac{35-\sqrt{{(-35)}^{2}-4\times 4\times -36}}{2\times 4}\]
Simplify.
\[x=\frac{35+\sqrt{1801}}{8},\frac{35-\sqrt{1801}}{8}\]
\[x=\frac{35+\sqrt{1801}}{8},\frac{35-\sqrt{1801}}{8}\]
Decimal Form: 9.679774, -0.929774
x=(35+sqrt(1801))/8,(35-sqrt(1801))/8
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