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受欢迎的代数 >

completesquare 2x^2-14x+1=0

解答

2 x^{2} - 14 x + 1 = 0

解答

x = \frac{47 + 7}{2}, x = \frac{- 47 + 7}{2}

+1

十进制

x = 6.92782 \dots, x = 0.07217 \dots

求解步骤

2 x^{2} - 14 x + 1 = 0

将

1

到右边

2 x^{2} - 14 x = - 1

两边除以

2

\frac{2 x ^{2} - 14 x}{2} = \frac{- 1}{2}

x^{2} - 7 x = - \frac{1}{2}

改写为形式

(x + a)^{2} = b

(x - \frac{7}{2})^{2} = \frac{47}{4}

若

f^{2} (x) = a

，解为

f (x) = a, - a

解

x - \frac{7}{2} = \frac{47}{4} : x = \frac{47 + 7}{2}

解

x - \frac{7}{2} = - \frac{47}{4} : x = \frac{- 47 + 7}{2}

二次方程组的解是:

x = \frac{47 + 7}{2}, x = \frac{- 47 + 7}{2}

作图

流行的例子

25 x^{2} + 50 x + 25 = 0

completesquare 2x^2+2x-2=0

co m pl e t es q u a re 2 x^{2} + 2 x - 2 = 0

solvefor x,x^2+y^2-(z^2)/4 =1

so l v e f or x, x^{2} + y^{2} - \frac{z ^{2}}{4} = 1

solvefor a,a^2+b^2+1=ab+a+b

so l v e f or a, a^{2} + b^{2} + 1 = ab + a + b

solvefor x,5x^2-15x=0

so l v e f or x, 5 x^{2} - 15 x = 0