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受欢迎的代数 >

k^2x^2+6x=(k+6)x^2-k

解答

k^{2} x^{2} + 6 x = (k + 6) x^{2} - k

解答

x = \frac{- 3 + - k ( k ^{2} - k - 6 ) + 9}{k ^{2} - k - 6}, x = - \frac{- k ( k ^{2} - k - 6 ) + 9 + 3}{k ^{2} - k - 6}; k \neq = 3, k \neq = - 2

求解步骤

k^{2} x^{2} + 6 x = (k + 6) x^{2} - k

将

k

para o lado esquerdo

k^{2} x^{2} + 6 x + k = (k + 6) x^{2}

将

(k + 6) x^{2}

para o lado esquerdo

k^{2} x^{2} + 6 x + k - (k + 6) x^{2} = 0

改写成标准形式

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

(k^{2} - k - 6) x^{2} + 6 x + k = 0

使用求根公式求解

x_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 ( k ^{2} - k - 6 ) k}{2 ( k ^{2} - k - 6 )}

化简

6^{2} - 4 (k^{2} - k - 6) k : 2 9 - k (k^{2} - 6 - k)

x_{1, 2} = \frac{- 6 \pm 2 9 - k ( k ^{2} - 6 - k )}{2 ( k ^{2} - k - 6 )}; k \neq = 3, k \neq = - 2

将解分隔开

x_{1} = \frac{- 6 + 2 9 - k ( k ^{2} - 6 - k )}{2 ( k ^{2} - k - 6 )}, x_{2} = \frac{- 6 - 2 9 - k ( k ^{2} - 6 - k )}{2 ( k ^{2} - k - 6 )}

x = \frac{- 6 + 2 9 - k ( k ^{2} - 6 - k )}{2 ( k ^{2} - k - 6 )} : \frac{- 3 + - k ( k ^{2} - k - 6 ) + 9}{k ^{2} - k - 6}

x = \frac{- 6 - 2 9 - k ( k ^{2} - 6 - k )}{2 ( k ^{2} - k - 6 )} : - \frac{- k ( k ^{2} - k - 6 ) + 9 + 3}{k ^{2} - k - 6}

二次方程组的解是:

x = \frac{- 3 + - k ( k ^{2} - k - 6 ) + 9}{k ^{2} - k - 6}, x = - \frac{- k ( k ^{2} - k - 6 ) + 9 + 3}{k ^{2} - k - 6}; k \neq = 3, k \neq = - 2

作图

流行的例子

81 x^{2} - 289 = 0

0 = - x^{2} + 3 x + 28

x^{2} - x = \frac{1}{3}

x^{2} + 2 x + 7 = 15

solvefor x,0=-0.02x^2+x+2.6

so l v e f or x, 0 = - 0.02 x^{2} + x + 2.6