Algebra 2 helppppp?

Question

complete the square and find all the solutions to the equation 
x^2+2x+2=5 

x^2+6x+10=17 

x^2+10x+20=31

Answer 1

1) The equation x² + 2x + 2  = 5

Separate variables and constants aside by subtracting 2 from each side.

x² + 2x = 3

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 2. so, (half the x coefficient)² = (2/2)²= 1

Add 1 to each side

x² + 2x + 1 = 3 + 1

(x + 1)²= 4

Take square root both sides

x + 1 = ±√4

x  = ± 2 - 1

x = 1, - 3

Solutions are x = 1, - 3.

 

2) The equation x² + 6x + 10 = 17

Separate variables and constants aside by subtracting 10 from each side.

x² + 6x  = 7

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 6. so, (half the x coefficient)² = (6/2)²= 9

Add 9 to each side

x² + 6x  + 9 = 7 + 9

(x + 3)²= 16

Take square root both sides

x + 3 = ± √16

x = - 3 ± 4

x = -3 + 4 and x = -3 - 4

Solutions are x = 1 and x = - 7

 

3) The equation x² + 10x + 20 = 31

Separate variables and constants aside by subtracting 20 from each side.

x² + 10x = 11

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 10. so, (half the x coefficient)² = (10/2)²= 25

Add 25 to each side

x² + 10x + 25 = 11 + 25

(x + 5)²= 36

Take square root both sides

x + 5 = ±√36

x = - 5 ± 6

x = - 5 + 6 and x = - 5 - 6

Solutions are x = 1 and x = - 11.