What are the solutions to the equation (x+3)^2+4(x+2)^2=25^2 ?

The solutions to the equation (x+3)^2+4(x+2)^2=25^2 are x=(-11+sqrt(3121))/5 ,x=-(11+sqrt(3121))/5

Find the zeros of (x+3)^2+4(x+2)^2=25^2

The zeros of (x+3)^2+4(x+2)^2=25^2 are x=(-11+sqrt(3121))/5 ,x=-(11+sqrt(3121))/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x + 3)^{2} + 4 (x + 2)^{2} = 2 5^{2}

x = \frac{- 11 + 3121}{5}, x = - \frac{11 + 3121}{5}

Decimal Notation

x = 8.97318 \dots, x = - 13.37318 \dots

Solution steps

(x + 3)^{2} + 4 (x + 2)^{2} = 2 5^{2}

Expand

(x + 3)^{2} + 4 (x + 2)^{2} : 5 x^{2} + 22 x + 25

Expand

2 5^{2} : 625

5 x^{2} + 22 x + 25 = 625

Move

625

to the left side

5 x^{2} + 22 x - 600 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 22 \pm 2 2 ^{2} - 4 \cdot 5 ( - 600 )}{2 \cdot 5}

2 2^{2} - 4 \cdot 5 (- 600) = 23121

x_{1, 2} = \frac{- 22 \pm 2 3121}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- 22 + 2 3121}{2 \cdot 5}, x_{2} = \frac{- 22 - 2 3121}{2 \cdot 5}

x = \frac{- 22 + 2 3121}{2 \cdot 5} : \frac{- 11 + 3121}{5}

x = \frac{- 22 - 2 3121}{2 \cdot 5} : - \frac{11 + 3121}{5}

The solutions to the quadratic equation are:

x = \frac{- 11 + 3121}{5}, x = - \frac{11 + 3121}{5}

5 = 3 x^{2}

x, x^{2} - 10 x + 20 = 0

(3 - 2 x)^{2} = 7

2 x^{2} = - 4 x

y^{2} - 15 y = - 54

What are the solutions to the equation (x+3)^2+4(x+2)^2=25^2 ?
The solutions to the equation (x+3)^2+4(x+2)^2=25^2 are x=(-11+sqrt(3121))/5 ,x=-(11+sqrt(3121))/5
Find the zeros of (x+3)^2+4(x+2)^2=25^2
The zeros of (x+3)^2+4(x+2)^2=25^2 are x=(-11+sqrt(3121))/5 ,x=-(11+sqrt(3121))/5