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Popular >

(a-x)/b =c(x-d)^2

Solution

\frac{a - x}{b} = c (x - d)^{2}

Solution

x = \frac{2 b c d - 1 + 4 ab c - 4 b c d + 1}{2 b c}, x = \frac{2 b c d - 1 - 4 ab c - 4 b c d + 1}{2 b c}; b c \neq = 0

Solution steps

\frac{a - x}{b} = c (x - d)^{2}

Multiply both sides by

b

a - x = b c (x - d)^{2}; b \neq = 0

Expand

b c (x - d)^{2} : b c x^{2} - 2 b c d x + b c d^{2}

a - x = b c x^{2} - 2 b c d x + b c d^{2}; b \neq = 0

Switch sides

b c x^{2} - 2 b c d x + b c d^{2} = a - x; b \neq = 0

Move

x

to the left side

b c x^{2} - 2 b c d x + b c d^{2} + x = a; b \neq = 0

Move

a

to the left side

b c x^{2} - 2 b c d x + b c d^{2} + x - a = 0; b \neq = 0

Write in the standard form

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

b c x^{2} + (- 2 b c d + 1) x + b c d^{2} - a = 0; b \neq = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 b c d + 1 ) \pm ( - 2 b c d + 1 ) ^{2} - 4 b c ( b c d ^{2} - a )}{2 b c}

Simplify

(- 2 b c d + 1)^{2} - 4 b c (b c d^{2} - a) : 4 ab c - 4 b c d + 1

x_{1, 2} = \frac{- ( - 2 b c d + 1 ) \pm 4 ab c - 4 b c d + 1}{2 b c}; b c \neq = 0

Separate the solutions

x_{1} = \frac{- ( - 2 b c d + 1 ) + 4 ab c - 4 b c d + 1}{2 b c}, x_{2} = \frac{- ( - 2 b c d + 1 ) - 4 ab c - 4 b c d + 1}{2 b c}

x = \frac{- ( - 2 b c d + 1 ) + 4 ab c - 4 b c d + 1}{2 b c} : \frac{2 b c d - 1 + 4 ab c - 4 b c d + 1}{2 b c}

x = \frac{- ( - 2 b c d + 1 ) - 4 ab c - 4 b c d + 1}{2 b c} : \frac{2 b c d - 1 - 4 ab c - 4 b c d + 1}{2 b c}

The solutions to the quadratic equation are:

x = \frac{2 b c d - 1 + 4 ab c - 4 b c d + 1}{2 b c}, x = \frac{2 b c d - 1 - 4 ab c - 4 b c d + 1}{2 b c}; b c \neq = 0

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