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Popular Algebra >

solvefor x,(x^2)/(c^2)-(y^9)/(d^2)=pix

Solution

solve for

x, \frac{x ^{2}}{c ^{2}} - \frac{y ^{9}}{d ^{2}} = π x

Solution

x = \frac{c ( π c d + 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}, x = \frac{c ( π c d - 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}; d \neq = 0

Solution steps

\frac{x ^{2}}{c ^{2}} - \frac{y ^{9}}{d ^{2}} = π x

Find Least Common Multiplier of

c^{2}, d^{2} : c^{2} d^{2}

Multiply by LCM=

c^{2} d^{2}

\frac{x ^{2}}{c ^{2}} c^{2} d^{2} - \frac{y ^{9}}{d ^{2}} c^{2} d^{2} = π x c^{2} d^{2}; c^{2} d^{2} \neq = 0

Simplify

d^{2} x^{2} - c^{2} y^{9} = π c^{2} d^{2} x; c^{2} d^{2} \neq = 0

Move

π c^{2} d^{2} x

to the left side

d^{2} x^{2} - c^{2} y^{9} - π c^{2} d^{2} x = 0; c^{2} d^{2} \neq = 0

Write in the standard form

a x^{2} + b x + c = 0

d^{2} x^{2} - π c^{2} d^{2} x - c^{2} y^{9} = 0; c^{2} d^{2} \neq = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - π c ^{2} d ^{2} ) \pm ( - π c ^{2} d ^{2} ) ^{2} - 4 d ^{2} ( - c ^{2} y ^{9} )}{2 d ^{2}}

Simplify

(- π c^{2} d^{2})^{2} - 4 d^{2} (- c^{2} y^{9}) : c d π^{2} c^{2} d^{2} + 4 y^{9}

x_{1, 2} = \frac{- ( - π c ^{2} d ^{2} ) \pm c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}}; d \neq = 0

Separate the solutions

x_{1} = \frac{- ( - π c ^{2} d ^{2} ) + c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}}, x_{2} = \frac{- ( - π c ^{2} d ^{2} ) - c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}}

x = \frac{- ( - π c ^{2} d ^{2} ) + c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}} : \frac{c ( π c d + 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}

x = \frac{- ( - π c ^{2} d ^{2} ) - c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}} : \frac{c ( π c d - 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}

The solutions to the quadratic equation are:

x = \frac{c ( π c d + 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}, x = \frac{c ( π c d - 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}; d \neq = 0

Graph

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