Solve a = a^2 b - c^2

Evaluate

a = a^{2} b - c^{2}

Rewrite the expression

a = b a^{2} - c^{2}

Move the expression to the left side

a - (b a^{2} - c^{2}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Rewrite in standard form

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

Substitute a= - b,b= 1 and c= c^{2} into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

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

Simplify the expression

More Steps

a = \frac{- 1 \pm 1 + 4 b c ^{2}}{- 2 b}

Separate the equation into 2 possible cases

a = \frac{- 1 + 1 + 4 b c ^{2}}{- 2 b} a = \frac{- 1 - 1 + 4 b c ^{2}}{- 2 b}

Simplify the expression

More Steps

a = \frac{1 - 1 + 4 b c ^{2}}{2 b} a = \frac{- 1 - 1 + 4 b c ^{2}}{- 2 b}

Solution

a = \frac{1 - 1 + 4 b c ^{2}}{2 b} a = \frac{1 + 1 + 4 b c ^{2}}{2 b}

Solve the equation