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人気のある代数 >

solvefor x,f(x+h)=2(x+h)^2+5(x+h)-3

解

解く

x, f (x + h) = 2 (x + h)^{2} + 5 (x + h) - 3

解

x = \frac{- 4 h - 5 + f + f ^{2} - 10 f + 49}{4}, x = \frac{- 4 h - 5 + f - f ^{2} - 10 f + 49}{4}

解答ステップ

f (x + h) = 2 (x + h)^{2} + 5 (x + h) - 3

拡張

f (x + h) : x f + h f

拡張

2 (x + h)^{2} + 5 (x + h) - 3 : 2 x^{2} + 4 x h + 2 h^{2} + 5 x + 5 h - 3

x f + h f = 2 x^{2} + 4 x h + 2 h^{2} + 5 x + 5 h - 3

辺を交換する

2 x^{2} + 4 x h + 2 h^{2} + 5 x + 5 h - 3 = x f + h f

h f

を左側に移動します

2 x^{2} + 4 x h + 2 h^{2} + 5 x + 5 h - 3 - h f = x f

x f

を左側に移動します

2 x^{2} + 4 x h + 2 h^{2} + 5 x + 5 h - 3 - h f - x f = 0

標準的な形式で書く

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

2 x^{2} + (4 h + 5 - f) x + 2 h^{2} + 5 h - 3 - h f = 0

解くとthe二次式

x_{1, 2} = \frac{- ( 4 h + 5 - f ) \pm ( 4 h + 5 - f ) ^{2} - 4 \cdot 2 ( 2 h ^{2} + 5 h - 3 - h f )}{2 \cdot 2}

簡素化

(4 h + 5 - f)^{2} - 4 \cdot 2 (2 h^{2} + 5 h - 3 - h f) : f^{2} - 10 f + 49

x_{1, 2} = \frac{- ( 4 h + 5 - f ) \pm f ^{2} - 10 f + 49}{2 \cdot 2}

解を分離する

x_{1} = \frac{- ( 4 h + 5 - f ) + f ^{2} - 10 f + 49}{2 \cdot 2}, x_{2} = \frac{- ( 4 h + 5 - f ) - f ^{2} - 10 f + 49}{2 \cdot 2}

x = \frac{- ( 4 h + 5 - f ) + f ^{2} - 10 f + 49}{2 \cdot 2} : \frac{- 4 h - 5 + f + f ^{2} - 10 f + 49}{4}

x = \frac{- ( 4 h + 5 - f ) - f ^{2} - 10 f + 49}{2 \cdot 2} : \frac{- 4 h - 5 + f - f ^{2} - 10 f + 49}{4}

二次equationの解:

x = \frac{- 4 h - 5 + f + f ^{2} - 10 f + 49}{4}, x = \frac{- 4 h - 5 + f - f ^{2} - 10 f + 49}{4}

グラフ

人気の例

y^{2} - 14 y + 4 = 0

(2 x + 3) (4 x + 5) = 0

solvefor x,(x-1)^2+(y-6)^2=25

so l v e f or x, (x - 1)^{2} + (y - 6)^{2} = 25

y^{2} + 5 y + 2 = 0

r^{2} - 16 r = 0