What are the solutions to the equation solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz ?

The solutions to the equation solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz are x=2-y-z,x=-y-z

Find the zeros of solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz

The zeros of solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz are x=2-y-z,x=-y-z

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solve for

x, (x + y + z) 2 = x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz

x = 2 - y - z, x = - y - z

Solution steps

(x + y + z) \cdot 2 = x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz

Expand

(x + y + z) \cdot 2 : 2 x + 2 y + 2 z

2 x + 2 y + 2 z = x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz

Switch sides

x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz = 2 x + 2 y + 2 z

Move

2 z

to the left side

x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz - 2 z = 2 x + 2 y

Move

2 y

to the left side

x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz - 2 z - 2 y = 2 x

Move

2 x

to the left side

x^{2} + y^{2} + z^{2} + 2 x y + 2 x z + 2 yz - 2 z - 2 y - 2 x = 0

Write in the standard form

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

x^{2} + (2 y + 2 z - 2) x + y^{2} + z^{2} + 2 yz - 2 z - 2 y = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 2 y + 2 z - 2 ) \pm ( 2 y + 2 z - 2 ) ^{2} - 4 \cdot 1 \cdot ( y ^{2} + z ^{2} + 2 yz - 2 z - 2 y )}{2 \cdot 1}

(2 y + 2 z - 2)^{2} - 4 \cdot 1 \cdot (y^{2} + z^{2} + 2 yz - 2 z - 2 y) = 2

x_{1, 2} = \frac{- ( 2 y + 2 z - 2 ) \pm 2}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( 2 y + 2 z - 2 ) + 2}{2 \cdot 1}, x_{2} = \frac{- ( 2 y + 2 z - 2 ) - 2}{2 \cdot 1}

x = \frac{- ( 2 y + 2 z - 2 ) + 2}{2 \cdot 1} : 2 - y - z

x = \frac{- ( 2 y + 2 z - 2 ) - 2}{2 \cdot 1} : - y - z

The solutions to the quadratic equation are:

x = 2 - y - z, x = - y - z

y = 2 (- 1)^{2}

- 3 = 7 (y - 79)

- \frac{1}{2} x - (\frac{1}{2} x + 4) + 12 = 17 x - 6 (3 x + \frac{5}{6})

5.2 w = - 2.08

7 x = 3 x + 36

What are the solutions to the equation solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz ?
The solutions to the equation solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz are x=2-y-z,x=-y-z
Find the zeros of solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz
The zeros of solvefor x,(x+y+z)2=x^2+y^2+z^2+2xy+2xz+2yz are x=2-y-z,x=-y-z