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人気のある代数 >

solvefor x,px^2+qx+r=(x+2)(x+2)

解

解く

x, p x^{2} + q x + r = (x + 2) (x + 2)

解

x = \frac{- q + 4 + 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}, x = \frac{- q + 4 - 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}; p \neq = 1

解答ステップ

p x^{2} + q x + r = (x + 2) (x + 2)

拡張

(x + 2) (x + 2) : x^{2} + 4 x + 4

p x^{2} + q x + r = x^{2} + 4 x + 4

4

を左側に移動します

p x^{2} + q x + r - 4 = x^{2} + 4 x

4 x

を左側に移動します

p x^{2} + q x + r - 4 - 4 x = x^{2}

x^{2}

を左側に移動します

p x^{2} + q x + r - 4 - 4 x - x^{2} = 0

標準的な形式で書く

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

(p - 1) x^{2} + (q - 4) x + r - 4 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( q - 4 ) \pm ( q - 4 ) ^{2} - 4 ( p - 1 ) ( r - 4 )}{2 ( p - 1 )}

簡素化

(q - 4)^{2} - 4 (p - 1) (r - 4) : 16 p - 4 p r + q^{2} + 4 r - 8 q

x_{1, 2} = \frac{- ( q - 4 ) \pm 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}; p \neq = 1

解を分離する

x_{1} = \frac{- ( q - 4 ) + 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}, x_{2} = \frac{- ( q - 4 ) - 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}

x = \frac{- ( q - 4 ) + 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )} : \frac{- q + 4 + 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}

x = \frac{- ( q - 4 ) - 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )} : \frac{- q + 4 - 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}

二次equationの解:

x = \frac{- q + 4 + 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}, x = \frac{- q + 4 - 16 p - 4 p r + q ^{2} + 4 r - 8 q}{2 ( p - 1 )}; p \neq = 1

グラフ

人気の例

3 x^{2} - 2 x + 9 = 4

x^2+(1-x)^2=5-(2-x)^2

x^{2} + (1 - x)^{2} = 5 - (2 - x)^{2}

- 1 x^{2} + 1 x + 12 = 0

(x + 3) (x - 0) = 0

4 = b^{2}