y^2+y-120=0

Simple and best practice solution for y^2+y-120=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for y^2+y-120=0 equation: 


Simplifying
y2 + y + -120 = 0

Reorder the terms:
-120 + y + y2 = 0

Solving
-120 + y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + y + 120 + y2 = 0 + 120

Reorder the terms:
-120 + 120 + y + y2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + y + y2 = 0 + 120
y + y2 = 0 + 120

Combine like terms: 0 + 120 = 120
y + y2 = 120

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
y + 0.25 + y2 = 120 + 0.25

Reorder the terms:
0.25 + y + y2 = 120 + 0.25

Combine like terms: 120 + 0.25 = 120.25
0.25 + y + y2 = 120.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(y + 0.5) equal to 10.9658561 and -10.9658561.


Subproblem 1
y + 0.5 = 10.9658561

Simplifying
y + 0.5 = 10.9658561

Reorder the terms:
0.5 + y = 10.9658561

Solving
0.5 + y = 10.9658561

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 10.9658561 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 10.9658561 + -0.5
y = 10.9658561 + -0.5

Combine like terms: 10.9658561 + -0.5 = 10.4658561
y = 10.4658561

Simplifying
y = 10.4658561


Subproblem 2
y + 0.5 = -10.9658561

Simplifying
y + 0.5 = -10.9658561

Reorder the terms:
0.5 + y = -10.9658561

Solving
0.5 + y = -10.9658561

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -10.9658561 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -10.9658561 + -0.5
y = -10.9658561 + -0.5

Combine like terms: -10.9658561 + -0.5 = -11.4658561
y = -11.4658561

Simplifying
y = -11.4658561


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.4658561, -11.4658561}

See similar equations:

| 375/500 | | 7k+8*7k-8=49k-64 | | 4(2)-3/2(-1)-1 | | 42/441 | | x=3/(1-0.7) | | 5+7b*5-7b=-49b+25 | | log^2(7x+5)=9 | | 2.25x+0.125+0.875=0.0625 | | -5r(-8+5r)=0 | | 2(y-1)+5y=9 | | 3x+(5-2x)+4=6 | | 3x+1y=33 | | -3+2=x+10 | | -1_-(g/10)-6 | | 2(a+1)2+3(a+1)-2=0 | | x^2-6x+100=0 | | 19y-4y+23= | | -16w+13y-4w= | | 6x+12=118-7x | | (0.4)(2a)-(0.4)(0.3b)= | | 87=5y^2 | | 0tox=2 | | -7m=5 | | -128-3x=110+11x | | -128-3x=110*11x | | x^2+y^2-4x-4y+6=0 | | 3y+(-9)=(-15) | | 1500+367x=16600 | | 6x+12y=14 | | 7b+2=-3+8b | | -82+8x=-10x+188 | | -(8x+3)=46 |

Equations solver categories