What are the solutions to the equation ((x+2)^2)/5+((x-2)^2)/3 = 16/3 ?

The solutions to the equation ((x+2)^2)/5+((x-2)^2)/3 = 16/3 are x=3,x=-2

Find the zeros of ((x+2)^2)/5+((x-2)^2)/3 = 16/3

The zeros of ((x+2)^2)/5+((x-2)^2)/3 = 16/3 are x=3,x=-2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{( x + 2 ) ^{2}}{5} + \frac{( x - 2 ) ^{2}}{3} = \frac{16}{3}

x = 3, x = - 2

Solution steps

\frac{( x + 2 ) ^{2}}{5} + \frac{( x - 2 ) ^{2}}{3} = \frac{16}{3}

Find Least Common Multiplier of

5, 3 : 15

Multiply by LCM=

15

\frac{( x + 2 ) ^{2}}{5} \cdot 15 + \frac{( x - 2 ) ^{2}}{3} \cdot 15 = \frac{16}{3} \cdot 15

Simplify

3 (x + 2)^{2} + 5 (x - 2)^{2} = 80

Expand

3 (x + 2)^{2} + 5 (x - 2)^{2} : 8 x^{2} - 8 x + 32

8 x^{2} - 8 x + 32 = 80

Move

80

to the left side

8 x^{2} - 8 x - 48 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 8 ( - 48 )}{2 \cdot 8}

(- 8)^{2} - 4 \cdot 8 (- 48) = 40

x_{1, 2} = \frac{- ( - 8 ) \pm 40}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 40}{2 \cdot 8}, x_{2} = \frac{- ( - 8 ) - 40}{2 \cdot 8}

x = \frac{- ( - 8 ) + 40}{2 \cdot 8} : 3

x = \frac{- ( - 8 ) - 40}{2 \cdot 8} : - 2

The solutions to the quadratic equation are:

x = 3, x = - 2

x^{2} - x - 1

(x - 5)^{2} = - 25

2 x^{2} - 7 x + 5

12 x^{2} - 30 x = 0

4 x^{2} - 1 = 15

What are the solutions to the equation ((x+2)^2)/5+((x-2)^2)/3 = 16/3 ?
The solutions to the equation ((x+2)^2)/5+((x-2)^2)/3 = 16/3 are x=3,x=-2
Find the zeros of ((x+2)^2)/5+((x-2)^2)/3 = 16/3
The zeros of ((x+2)^2)/5+((x-2)^2)/3 = 16/3 are x=3,x=-2