Solve dg = da - (l/a) * dl

Question

Solve the equation

Solve for a

Solve for d

Solve for g

a = \frac{g + g ^{2} + 4 l ^{2}}{2} a = \frac{g - g ^{2} + 4 l ^{2}}{2}

Evaluate

d g = d a - \frac{l}{a} \times d l

Multiply the terms

More Steps

d g = d a - \frac{l ^{2} d}{a}

Swap the sides of the equation

d a - \frac{l ^{2} d}{a} = d g

Multiply both sides of the equation by LCD

(d a - \frac{l ^{2} d}{a}) a = d g a

Simplify the equation

More Steps

d a^{2} - l^{2} d = d g a

Move the expression to the left side

d a^{2} - l^{2} d - d g a = 0

Rewrite in standard form

d a^{2} - d g a - l^{2} d = 0

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

a = \frac{d g \pm ( - d g ) ^{2} - 4 d ( - l ^{2} d )}{2 d}

Simplify the expression

More Steps

a = \frac{d g \pm d ^{2} g ^{2} + 4 d ^{2} l ^{2}}{2 d}

Simplify the radical expression

More Steps

a = \frac{d g \pm d g ^{2} + 4 l ^{2}}{2 d}

Separate the equation into 2 possible cases

a = \frac{d g + d g ^{2} + 4 l ^{2}}{2 d} a = \frac{d g - d g ^{2} + 4 l ^{2}}{2 d}

Simplify the expression

More Steps

a = \frac{g + g ^{2} + 4 l ^{2}}{2} a = \frac{d g - d g ^{2} + 4 l ^{2}}{2 d}

Solution

More Steps

a = \frac{g + g ^{2} + 4 l ^{2}}{2} a = \frac{g - g ^{2} + 4 l ^{2}}{2}

Show Solution