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受欢迎的代数 >

solvefor y,9x^2-4y^2-36x-16y+20=0

解答

求解

y, 9 x^{2} - 4 y^{2} - 36 x - 16 y + 20 = 0

解答

y = - \frac{3 x - 2}{2}, y = - \frac{- 3 x + 10}{2}

求解步骤

9 x^{2} - 4 y^{2} - 36 x - 16 y + 20 = 0

改写成标准形式

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

- 4 y^{2} - 16 y + 9 x^{2} - 36 x + 20 = 0

使用求根公式求解

y_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 ( - 4 ) ( 9 x ^{2} - 36 x + 20 )}{2 ( - 4 )}

化简

(- 16)^{2} - 4 (- 4) (9 x^{2} - 36 x + 20) : 12 (x - 2)

y_{1, 2} = \frac{- ( - 16 ) \pm 12 ( x - 2 )}{2 ( - 4 )}

将解分隔开

y_{1} = \frac{- ( - 16 ) + 12 ( x - 2 )}{2 ( - 4 )}, y_{2} = \frac{- ( - 16 ) - 12 ( x - 2 )}{2 ( - 4 )}

y = \frac{- ( - 16 ) + 12 ( x - 2 )}{2 ( - 4 )} : - \frac{3 x - 2}{2}

y = \frac{- ( - 16 ) - 12 ( x - 2 )}{2 ( - 4 )} : - \frac{- 3 x + 10}{2}

二次方程组的解是:

y = - \frac{3 x - 2}{2}, y = - \frac{- 3 x + 10}{2}

作图

流行的例子

4 x^{2} - x - 1 = 5

40 = 30 t - 5 t^{2}

solvefor f,f(1-x)=x^2-2x

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

4x^2+8x+3=a(x+b)^2+e

4 x^{2} + 8 x + 3 = a (x + b)^{2} + e

completesquare 2x^2=-6+8x

co m pl e t es q u a re 2 x^{2} = - 6 + 8 x