y+111=y*y

Simple and best practice solution for y+111=y*y 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+111=y*y equation:


Simplifying
y + 111 = y * y

Reorder the terms:
111 + y = y * y

Multiply y * y
111 + y = y2

Solving
111 + y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
111 + y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-111 + -1y + y2 = 0

Move the constant term to the right:

Add '111' to each side of the equation.
-111 + -1y + 111 + y2 = 0 + 111

Reorder the terms:
-111 + 111 + -1y + y2 = 0 + 111

Combine like terms: -111 + 111 = 0
0 + -1y + y2 = 0 + 111
-1y + y2 = 0 + 111

Combine like terms: 0 + 111 = 111
-1y + y2 = 111

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.
-1y + 0.25 + y2 = 111 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 111 + 0.25

Combine like terms: 111 + 0.25 = 111.25
0.25 + -1y + y2 = 111.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 111.25

Calculate the square root of the right side: 10.547511555

Break this problem into two subproblems by setting 
(y + 0.5) equal to 10.547511555 and -10.547511555.

Subproblem 1

y + 0.5 = 10.547511555 Simplifying y + 0.5 = 10.547511555 Reorder the terms: 0.5 + y = 10.547511555 Solving 0.5 + y = 10.547511555 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 = 10.547511555 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 10.547511555 + -0.5 y = 10.547511555 + -0.5 Combine like terms: 10.547511555 + -0.5 = 10.047511555 y = 10.047511555 Simplifying y = 10.047511555

Subproblem 2

y + 0.5 = -10.547511555 Simplifying y + 0.5 = -10.547511555 Reorder the terms: 0.5 + y = -10.547511555 Solving 0.5 + y = -10.547511555 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 = -10.547511555 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -10.547511555 + -0.5 y = -10.547511555 + -0.5 Combine like terms: -10.547511555 + -0.5 = -11.047511555 y = -11.047511555 Simplifying y = -11.047511555

Solution

The solution to the problem is based on the solutions from the subproblems. y = {10.047511555, -11.047511555}

See similar equations:

| x^2+14x-5=0 | | y=8(-1) | | 2x+32=10x-4 | | 3x-9=-2+16 | | 3x-9=-2x | | 127-2x=43x+17 | | 5x-6=4x+4 | | 3(x-6)=12 | | 5x+1=14x+82 | | 5x-y(3x-y)= | | 6x(x-1)=0 | | (35x-30y)+(46x+63y)= | | (x+3)(x+16)=0 | | 27750.00+200.00x=312.50x | | 3p+3=3-2p | | (2X+1)0.33=1 | | 59+5x=11+11x | | (x-8)(x+2)=0 | | [x]=9 | | 14-2+4x=20 | | 5y-5=y+19 | | x^5+6x^3+9x=0 | | 4x-7=x+23 | | 134-3x=33x+22 | | 27750.00+200.00x=50000 | | (5x-3)(3x+3)= | | 4x-2=6(2x-4)-8 | | 2(3m-6+3m)=2m+2-4m | | x^3-25=0 | | 2(3m-6+3m)-7m=8 | | 11=17x-9 | | 11=17(1)-9 |

Equations solver categories