y^2+y-54=0

Simple and best practice solution for y^2+y-54=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-54=0 equation: 


Simplifying
y2 + y + -54 = 0

Reorder the terms:
-54 + y + y2 = 0

Solving
-54 + y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + y + 54 + y2 = 0 + 54

Reorder the terms:
-54 + 54 + y + y2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + y + y2 = 0 + 54
y + y2 = 0 + 54

Combine like terms: 0 + 54 = 54
y + y2 = 54

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 = 54 + 0.25

Reorder the terms:
0.25 + y + y2 = 54 + 0.25

Combine like terms: 54 + 0.25 = 54.25
0.25 + y + y2 = 54.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(y + 0.5) equal to 7.365459931 and -7.365459931.


Subproblem 1
y + 0.5 = 7.365459931

Simplifying
y + 0.5 = 7.365459931

Reorder the terms:
0.5 + y = 7.365459931

Solving
0.5 + y = 7.365459931

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 = 7.365459931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 7.365459931 + -0.5
y = 7.365459931 + -0.5

Combine like terms: 7.365459931 + -0.5 = 6.865459931
y = 6.865459931

Simplifying
y = 6.865459931


Subproblem 2
y + 0.5 = -7.365459931

Simplifying
y + 0.5 = -7.365459931

Reorder the terms:
0.5 + y = -7.365459931

Solving
0.5 + y = -7.365459931

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 = -7.365459931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -7.365459931 + -0.5
y = -7.365459931 + -0.5

Combine like terms: -7.365459931 + -0.5 = -7.865459931
y = -7.865459931

Simplifying
y = -7.865459931


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.865459931, -7.865459931}

See similar equations:

| (-1/4)x-1=-9 | | 2x+-4y=-12 | | 119=10x+59 | | 0.03X^2-33X+15000=28000 | | 20-2x=3-x | | 2-5+14=11 | | 4(2x-5)+8(3x-5)=5(4x-3)-3(2x-3) | | 600000-50-79000=130000 | | 350-70a=3 | | 898000+2= | | 50+111100+20= | | 290+890+78890+12390= | | -x/6+11=20 | | 3880+789789890= | | x+.15x=1200 | | 15+5+5+5= | | 7O= | | 5(P+4)-2(3p+2)=19 | | (x25)/8=5 | | 5(3x-4)=28-x | | 5-9+1-7=-10 | | 1d=33 | | 1408.42e^-4x/7=0.025 | | 400-28=372 | | 9+1+1+1+1+1+1+1+1=17 | | 12+11-5=2 | | 24Y+8=17.67 | | 12+10=22 | | 4x-1/3x^3 | | P(T)=P(0)*2 | | 3X-1+2X+1=3-X | | n+25=(13.9-27.8) |

Equations solver categories