how do you solve this equation (10 pts)?

Question

(y+1)^2 + y^2 = 113
plz show your work
thnx

Answer 1

First expand (y+1)^2
(y+1)^2 =y^2 +2y +1

Sub this in and get y^2 + 2y +1 +y^2 =113
Move the 113 over to the left and combine like terms
2y^2 +2y -112 =0
divide out the GCF of 2
y^2 + y - 56 =0
Factor: (y-7)(y+8) =0
y-7 =0
y= 7
y+8 =0
y = -8
the answers are 7 and -8

Answer 2

Solve for "y"... (y+1)^2 + y^2 = 113

First: express "y+1" in lowest terms, excluding the y-variables....

(y+1)(y+1) + y^2 = 113

*Eliminate parenthesis --- use the Foiling Method.....

(y)(y) + (y)(1) + (1)(y) + (1)(1) + y^2 = 113
y^2 + y + y + 1 + y^2 = 113

Sec: combine "like" terms....

y^2 + y^2 + y + y + 1 = 113
2y^2 + 2y + 1 = 113

Third: set the equation to "0" --- subtract 113 from both sides....

2y^2 + 2y + 1 - 113 = 113 - 113
2y^2 + 2y - 112 = 0

Fourth: factor the equation....

2(y^2 + y - 56) = 0

*Factor the expression in parenthesis - multiply the 1sy & 3rd coefficient to get "-56." Find two numbers that give you "-56" when multiplied & "1" (2nd/middle coefficient) when added/subtracted. The numbers are (8 & -7).

y^2 + 8y - 7y - 56

*With 4 terms - group "like" terms & factor both sets....

(y^2 + 8y) - (7y - 56)
y(y + 8) - 7(y + 8)
(y + 8)(y - 7)

Now, you have.... 2(y + 8)(y - 7) = 0

Fifth: solve the x-variables > set both parenthesis to "0"....

a. y + 8 = 0
*Isolate "y" on one side - subtract 8 from both sides....

y + 8 - 8 = 0 - 8
y = -8

b. y - 7 = 0
*Isolate "y" on one side - add 7 with both sides...

y - 7 + 7 = 0 + 7
y = 7

Solutions: - 8 & 7

Answer 3

(y+1)^2 =y^2 +2y +1 So your equation becomes 2y^2+2y-112=0
or(dividing by 2) y^2+y-56=0 2nd degree equ.

y=((-1+- sqrt(1+224))/2 = (-1+-15)/2 y=-8 y=7

Answer 4

y^2+2y+1+y^2=113
2y^2 +2y -112=0 quaratic formula
a=2,b=2,c=-112
sqrt=mean square root
sqrt(b^2-4ac)=
sqrt(2^2-4*2*-112)=
sqrt(900)=30

so y= (minus b plus and minus sqrt(b^2-4ac))/2a
y=[-2+-30]/(2*2)
y==[-2+-30]/4
solutions are
y=[-2+30]/4
and
y=[-2-30]/4

so answer is
y=7
and y= -8
that took so long but that will help you to understand
or you can do like
2y^2 +2y -112=0
(2y-14)(y+8)=0( by factor)
so 2y-14=0 => 2y=14=>y=14/2=7
and y+8=0=>y=-8



good luck

Answer 5

y2+2y+1+y2=113
2y^2+2y+1=113
2y^2+2y-112=0
(y+8)(2y-14)=0
y+8=0 or 2y-14=0
y=-8 or y=7