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受欢迎的代数 >

(a-3x)^2+(3a+1)x=a^2+2a

解答

(a - 3 x)^{2} + (3 a + 1) x = a^{2} + 2 a

解答

x = \frac{3 a - 1 + 9 a ^{2} + 66 a + 1}{18}, x = \frac{3 a - 1 - 9 a ^{2} + 66 a + 1}{18}

求解步骤

(a - 3 x)^{2} + (3 a + 1) x = a^{2} + 2 a

展开

(a - 3 x)^{2} + (3 a + 1) x : 9 x^{2} - 3 a x + x + a^{2}

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

将

2 a

para o lado esquerdo

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

将

a^{2}

para o lado esquerdo

9 x^{2} - 3 a x + x - 2 a = 0

改写成标准形式

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

9 x^{2} + (- 3 a + 1) x - 2 a = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 3 a + 1 ) \pm ( - 3 a + 1 ) ^{2} - 4 \cdot 9 ( - 2 a )}{2 \cdot 9}

化简

(- 3 a + 1)^{2} - 4 \cdot 9 (- 2 a) : 9 a^{2} + 66 a + 1

x_{1, 2} = \frac{- ( - 3 a + 1 ) \pm 9 a ^{2} + 66 a + 1}{2 \cdot 9}

将解分隔开

x_{1} = \frac{- ( - 3 a + 1 ) + 9 a ^{2} + 66 a + 1}{2 \cdot 9}, x_{2} = \frac{- ( - 3 a + 1 ) - 9 a ^{2} + 66 a + 1}{2 \cdot 9}

x = \frac{- ( - 3 a + 1 ) + 9 a ^{2} + 66 a + 1}{2 \cdot 9} : \frac{3 a - 1 + 9 a ^{2} + 66 a + 1}{18}

x = \frac{- ( - 3 a + 1 ) - 9 a ^{2} + 66 a + 1}{2 \cdot 9} : \frac{3 a - 1 - 9 a ^{2} + 66 a + 1}{18}

二次方程组的解是:

x = \frac{3 a - 1 + 9 a ^{2} + 66 a + 1}{18}, x = \frac{3 a - 1 - 9 a ^{2} + 66 a + 1}{18}

作图

流行的例子

4 = 6 x + x^{2}

(x-3.5)^2+(0.268x-0.402)^2=4

(x - 3.5)^{2} + (0.268 x - 0.402)^{2} = 4

0 = 6 x^{2} + 18 x

completesquare-x^2+12x-32

co m pl e t es q u a re - x^{2} + 12 x - 32

9 w^{2} + 25 = - 30 w