What is the answer to x+2/x =-9/2 ?

The answer to x+2/x =-9/2 is x=-1/2 ,x=-4

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x+2/x =-9/2

x + \frac{2}{x} = - \frac{9}{2}

x = - \frac{1}{2}, x = - 4

Decimal Notation

x = - 0.5, x = - 4

Solution steps

x + \frac{2}{x} = - \frac{9}{2}

Multiply by LCM

2 x^{2} + 4 = - 9 x

Solve

2 x^{2} + 4 = - 9 x : x = - \frac{1}{2}, x = - 4

x = - \frac{1}{2}, x = - 4

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{2}, x = - 4

3 = \frac{12 \cdot x}{12 + x}

(\frac{a}{b}) = \frac{c}{d + x}

\frac{1}{5 x} = 5 x^{- 1}

\frac{- ( - 4 ) ^{2}}{a} = 3 a + 4 (- 4) + 1

\frac{8}{3 x - 1} = \frac{3}{x + 4}