What are the solutions to the equation 2ax-x^2=-4a^2 ?

The solutions to the equation 2ax-x^2=-4a^2 are x=-(sqrt(5)-1)a,x=(1+sqrt(5))a

Find the zeros of 2ax-x^2=-4a^2

The zeros of 2ax-x^2=-4a^2 are x=-(sqrt(5)-1)a,x=(1+sqrt(5))a

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2 a x - x^{2} = - 4 a^{2}

x = - (5 - 1) a, x = (1 + 5) a

Solution steps

2 a x - x^{2} = - 4 a^{2}

Move

4 a^{2}

to the left side

2 a x - x^{2} + 4 a^{2} = 0

Write in the standard form

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

- x^{2} + 2 a x + 4 a^{2} = 0

Solve with the quadratic formula

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

Simplify

(2 a)^{2} - 4 (- 1) \cdot 4 a^{2} : 25 a

x_{1, 2} = \frac{- 2 a \pm 2 5 a}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 2 a + 2 5 a}{2 ( - 1 )}, x_{2} = \frac{- 2 a - 2 5 a}{2 ( - 1 )}

x = \frac{- 2 a + 2 5 a}{2 ( - 1 )} : - (5 - 1) a

x = \frac{- 2 a - 2 5 a}{2 ( - 1 )} : (1 + 5) a

The solutions to the quadratic equation are:

x = - (5 - 1) a, x = (1 + 5) a

v^{2} + 5 v + 28 = 0

4 u^{2} + 20 u = 0

x^{2} + 13 x - 36 = 0

2 x^{2} - 24 x + 64 = 0

2 x^{2} - 10 x = 12

What are the solutions to the equation 2ax-x^2=-4a^2 ?
The solutions to the equation 2ax-x^2=-4a^2 are x=-(sqrt(5)-1)a,x=(1+sqrt(5))a
Find the zeros of 2ax-x^2=-4a^2
The zeros of 2ax-x^2=-4a^2 are x=-(sqrt(5)-1)a,x=(1+sqrt(5))a