10y-y^2=5

Simple and best practice solution for 10y-y^2=5 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 10y-y^2=5 equation:


Simplifying
10y + -1y2 = 5

Solving
10y + -1y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + 10y + -1y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 10y + -1y2 = 0

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

Divide each side by '-1'.
5 + -10y + y2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -10y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + -10y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -10y + y2 = 0 + -5
-10y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-10y + y2 = -5

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 = -5 + 25

Reorder the terms:
25 + -10y + y2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + -10y + y2 = 20

Factor a perfect square on the left side:
(y + -5)(y + -5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(y + -5) equal to 4.472135955 and -4.472135955.

Subproblem 1

y + -5 = 4.472135955 Simplifying y + -5 = 4.472135955 Reorder the terms: -5 + y = 4.472135955 Solving -5 + y = 4.472135955 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 = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.472135955 + 5 y = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 y = 9.472135955 Simplifying y = 9.472135955

Subproblem 2

y + -5 = -4.472135955 Simplifying y + -5 = -4.472135955 Reorder the terms: -5 + y = -4.472135955 Solving -5 + y = -4.472135955 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 = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.472135955 + 5 y = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 y = 0.527864045 Simplifying y = 0.527864045

Solution

The solution to the problem is based on the solutions from the subproblems. y = {9.472135955, 0.527864045}

See similar equations:

| [(5m^2+4m-2)-(8m^2-2m+4)]-(m^2+m+6)=0 | | 12x-9=9x+3 | | 7(7x-(2-7y+2x)+7y)= | | 13-7x=123-42x | | 9g-g= | | 28+5(x-3)=13 | | w-9.5=15 | | 2x+3+3x+5= | | 72-4x=9x+20 | | m+2=11 | | 12+3(x+4)=24 | | 6+9x=46+x | | -3p=-12 | | 5(x-6)-10=4x+22 | | 2x+19=11x-89 | | 9x+6=4x+36 | | 2n= | | 11x-19=7x+5 | | 5x^2-2x+7=3 | | 10-8x=85-43x | | -6x+8=x+10-7x | | 2x^2+2=12 | | 11x-22=110 | | 0.4x^3-6x^2+5x+3=0 | | x^3+3x-5=0 | | 26=-5y+6 | | -n+7=12 | | -1=-4c-9 | | 4x+6=3x+6 | | 14=-c-14 | | x^2-6x-22=0 | | 9x^2-16y^2=144 |

Equations solver categories