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人気のある代数 >

solvefor x,x^2-6x+7=m(2x-3)

解

x, x^{2} - 6 x + 7 = m (2 x - 3)

解

x = 3 + m + m^{2} + 3 m + 2, x = 3 + m - m^{2} + 3 m + 2

解答ステップ

x^{2} - 6 x + 7 = m (2 x - 3)

拡張

m (2 x - 3) : 2 m x - 3 m

x^{2} - 6 x + 7 = 2 m x - 3 m

両辺から

2 m x - 3 m

を引く

x^{2} - 6 x + 7 - (2 m x - 3 m) = 2 m x - 3 m - (2 m x - 3 m)

簡素化

x^{2} - (6 + 2 m) x + 7 + 3 m = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 6 - 2 m ) \pm ( - 6 - 2 m ) ^{2} - 4 \cdot 1 \cdot ( 7 + 3 m )}{2 \cdot 1}

簡素化

(- 6 - 2 m)^{2} - 4 \cdot 1 \cdot (7 + 3 m) : 2 m^{2} + 3 m + 2

x_{1, 2} = \frac{- ( - 6 - 2 m ) \pm 2 m ^{2} + 3 m + 2}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( - 6 - 2 m ) + 2 m ^{2} + 3 m + 2}{2 \cdot 1}, x_{2} = \frac{- ( - 6 - 2 m ) - 2 m ^{2} + 3 m + 2}{2 \cdot 1}

x = \frac{- ( - 6 - 2 m ) + 2 m ^{2} + 3 m + 2}{2 \cdot 1} : 3 + m + m^{2} + 3 m + 2

x = \frac{- ( - 6 - 2 m ) - 2 m ^{2} + 3 m + 2}{2 \cdot 1} : 3 + m - m^{2} + 3 m + 2

二次equationの解:

x = 3 + m + m^{2} + 3 m + 2, x = 3 + m - m^{2} + 3 m + 2

グラフ

人気の例

x^{2} + 7 + 12 = 0

solvefor a,(a+2)^2+5=(b+2)^2+5

so l v e f or a, (a + 2)^{2} + 5 = (b + 2)^{2} + 5

solvefor x,s(x)=x(x-3)

so l v e f or x, s (x) = x (x - 3)

x^{2} - 125 = - 25

solvefor x,p=36x^2-9y^2

so l v e f or x, p = 36 x^{2} - 9 y^{2}