y(y+1)7=56

Simple and best practice solution for y(y+1)7=56 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(y+1)7=56 equation: 


Simplifying
y(y + 1) * 7 = 56

Reorder the terms:
y(1 + y) * 7 = 56

Reorder the terms for easier multiplication:
7y(1 + y) = 56
(1 * 7y + y * 7y) = 56
(7y + 7y2) = 56

Solving
7y + 7y2 = 56

Solving for variable 'y'.

Reorder the terms:
-56 + 7y + 7y2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + 7y + 7y2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + y + y2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-8 + y + y2)' equal to zero and attempt to solve:

Simplifying
-8 + y + y2 = 0

Solving
-8 + y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + y + y2 = 0 + 8
y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
y + y2 = 8

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 = 8 + 0.25

Reorder the terms:
0.25 + y + y2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + y + y2 = 8.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
y + 0.5 = 2.872281323

Simplifying
y + 0.5 = 2.872281323

Reorder the terms:
0.5 + y = 2.872281323

Solving
0.5 + y = 2.872281323

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 = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.872281323 + -0.5
y = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
y = 2.372281323

Simplifying
y = 2.372281323


Subproblem 2
y + 0.5 = -2.872281323

Simplifying
y + 0.5 = -2.872281323

Reorder the terms:
0.5 + y = -2.872281323

Solving
0.5 + y = -2.872281323

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 = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.872281323 + -0.5
y = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
y = -3.372281323

Simplifying
y = -3.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.372281323, -3.372281323}
Solution
y = {2.372281323, -3.372281323}

See similar equations:

| m(a-wb)=r | | 17y-14y=15 | | 12+7x=x+6 | | 112=-7(3m-1) | | (5x+-8)(3x+4)=140 | | 2(4x-3)+1=4(2x-1)+5 | | 5x-20=2x+37 | | y+y+1+7=56 | | (4x-4)=(5x+1) | | 3x^2+18xy+27y^2=0 | | 4-4y=-32 | | 19x-4x=17+2-1 | | 0.816*0.34= | | 9-y=y+3 | | -2j+4=12 | | 1-3x=4x+8 | | y-4=.5(x-8) | | 30x-10x=1.33333 | | (x-15)=80 | | 8x^2+16xy-6xy-12y^2=0 | | 3n-15=120 | | 6=2(h+8)-5h | | 4-6n=-8 | | 14-4z=34-4 | | -36-2x=5x-2(-3-7x) | | 12=9+7x-3x | | 10y-24=51+5y | | 9x+12=8x+6 | | log(x^3)=14 | | -72.8=5.6h | | (20x-15)=(15x+15) | | 5y+4=6 |

Equations solver categories