Question

Question 11 of 25

What is the solution to the equation below?
X+ 4 = V8 - x
O A. x = 0
B. X = -7
C. X = -1
D. X= 4

Answer 1

`{ \rm{x + 4 = √(8 - x) }} \\ \\ { \rm{ {(x + 4)}^(2) = {( √(8 - x)) }^(2) }} \\ \\ { \rm{(x + 4)(x + 4) = 8 - x}} \\ \\ { \rm{ {x}^(2) + 8x + 16 = 8 - x}} \\ \\ { \rm{ {x}^(2) + 9x + 8 = 0 }} \\ \\ { \rm{(x + 1)(x + 8) = 0}} \\ \\ { \boxed{ \tt{x _(1) = {}^( - ) 1}}} \: \: { \rm{and}} \: \: { \boxed{ \tt{x _(2) = {}^( - ) 8}}}`

Answer 2

`\\ \sf\longmapsto x+4=√(8-x)`

`\\ \sf\longmapsto (x+4)^2=8-x`

`\\ \sf\longmapsto x^2+16+8x=8-x`

`\\ \sf\longmapsto x^2+8x-x+16-8=0`

`\\ \sf\longmapsto x^2+7x+8=0`

`\\ \sf\longmapsto x^2-8x+x+8`

`\\ \sf\longmapsto (x-8)(x-1)=0`

`\\ \sf\longmapsto x=8,-1`

Option C