asqrt(x^2+d)+b=c

解

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

x = \frac{- d a ^{2} + c ^{2} - 2 b c + b ^{2}}{a}, x = - \frac{- d a ^{2} + c ^{2} - 2 b c + b ^{2}}{a}

解答ステップ

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

b

を右側に移動します

a x^{2} + d = c - b

以下で両辺を割る

a

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

両辺を2乗する:

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

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

解く

x^{2} + d = \frac{c ^{2}}{a ^{2}} - \frac{2 b c}{a ^{2}} + \frac{b ^{2}}{a ^{2}} : x = \frac{- d a ^{2} + c ^{2} - 2 b c + b ^{2}}{a}, x = - \frac{- d a ^{2} + c ^{2} - 2 b c + b ^{2}}{a}

x = \frac{- d a ^{2} + c ^{2} - 2 b c + b ^{2}}{a}, x = - \frac{- d a ^{2} + c ^{2} - 2 b c + b ^{2}}{a}