y^2-10y=-1

Simple and best practice solution for y^2-10y=-1 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^2-10y=-1 equation: 


Simplifying
y2 + -10y = -1

Reorder the terms:
-10y + y2 = -1

Solving
-10y + y2 = -1

Solving for variable 'y'.

Reorder the terms:
1 + -10y + y2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -10y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -10y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10y + y2 = 0 + -1
-10y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10y + y2 = -1

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = -1 + 25

Reorder the terms:
25 + -10y + y2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + -10y + y2 = 24

Factor a perfect square on the left side:
(y + -5)(y + -5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(y + -5) equal to 4.898979486 and -4.898979486.


Subproblem 1
y + -5 = 4.898979486

Simplifying
y + -5 = 4.898979486

Reorder the terms:
-5 + y = 4.898979486

Solving
-5 + y = 4.898979486

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 4.898979486 + 5

Combine like terms: -5 + 5 = 0
0 + y = 4.898979486 + 5
y = 4.898979486 + 5

Combine like terms: 4.898979486 + 5 = 9.898979486
y = 9.898979486

Simplifying
y = 9.898979486


Subproblem 2
y + -5 = -4.898979486

Simplifying
y + -5 = -4.898979486

Reorder the terms:
-5 + y = -4.898979486

Solving
-5 + y = -4.898979486

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -4.898979486 + 5

Combine like terms: -5 + 5 = 0
0 + y = -4.898979486 + 5
y = -4.898979486 + 5

Combine like terms: -4.898979486 + 5 = 0.101020514
y = 0.101020514

Simplifying
y = 0.101020514


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.898979486, 0.101020514}

See similar equations:

| 4x+6(5x-11)=172 | | 20x+-69=31 | | 3y-2(4y-108)=10y+16 | | 10x+x-68=108 | | 76x-65=87 | | 29x-63=82 | | -9x+12x-23=13 | | .06t-2.9=7 | | 16+(122+9)+9= | | .09d-.14=.67 | | 12xy-8xy= | | 2x+26=5x-10 | | 3-5y=15 | | -9-6x-7+8=7x-8 | | 2x+37=3x | | 50-2x=8-7x | | log^36(x)=0.5 | | -4(2-y)+3=3(y-4) | | (7y-3xz)squared= | | (9x+12)(2x-20)-64x=(3x-45)(6x-50)-90 | | xd=2x+7 | | 4(2x-3)4x= | | 18x^3+18x^2+4x-28=0 | | 155+60+x=180 | | 30+20+x=180 | | 102+137+x=180 | | 5x+2+8x+4+15x-19=180 | | 50+62+80+53+x=180 | | d=2(rv+rc+fc) | | 122+90+x=180 | | 6x+55=6x-40 | | 24x+12=11 |

Equations solver categories