0.5*y^2+10*y+5=0

Simple and best practice solution for 0.5*y^2+10*y+5=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 0.5*y^2+10*y+5=0 equation: 


Simplifying
0.5y2 + 10y + 5 = 0

Reorder the terms:
5 + 10y + 0.5y2 = 0

Solving
5 + 10y + 0.5y2 = 0

Solving for variable 'y'.

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

Divide each side by '0.5'.
10 + 20y + y2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 20y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + 20y + y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 20y + y2 = 0 + -10
20y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
20y + y2 = -10

The y term is 20y.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20y + 100 + y2 = -10 + 100

Reorder the terms:
100 + 20y + y2 = -10 + 100

Combine like terms: -10 + 100 = 90
100 + 20y + y2 = 90

Factor a perfect square on the left side:
(y + 10)(y + 10) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(y + 10) equal to 9.486832981 and -9.486832981.


Subproblem 1
y + 10 = 9.486832981

Simplifying
y + 10 = 9.486832981

Reorder the terms:
10 + y = 9.486832981

Solving
10 + y = 9.486832981

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = 9.486832981 + -10

Combine like terms: 10 + -10 = 0
0 + y = 9.486832981 + -10
y = 9.486832981 + -10

Combine like terms: 9.486832981 + -10 = -0.513167019
y = -0.513167019

Simplifying
y = -0.513167019


Subproblem 2
y + 10 = -9.486832981

Simplifying
y + 10 = -9.486832981

Reorder the terms:
10 + y = -9.486832981

Solving
10 + y = -9.486832981

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = -9.486832981 + -10

Combine like terms: 10 + -10 = 0
0 + y = -9.486832981 + -10
y = -9.486832981 + -10

Combine like terms: -9.486832981 + -10 = -19.486832981
y = -19.486832981

Simplifying
y = -19.486832981


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.513167019, -19.486832981}

See similar equations:

| 8-x+3x-2x-8x= | | 7x+5-8x=-1-4x-6 | | 0=42x | | 2y-2-2x=0 | | 1090=105x-209452 | | 9x^2+y^2-2y=80 | | 18-2=x | | [x-4]*2=169 | | (9x-6)/(21x-14) | | 0.5x+0.45(10)=0.25(72) | | 0-5x/-3 | | 1+8(M+2)=5M | | 0.3x+0.30(70)=0.15(48) | | x*x*x=x*x+105 | | 0.6x+6=36 | | (1)/(6)(9-y)12 | | -.8(a+3)=1.2(a+15) | | 3h*2-147=0 | | 6x-12+4x+32=180 | | 12y=3y-8*5 | | x+(0.1)x=50000 | | 3=x-55/11 | | -1.4=(x-62.5) | | x^6-x^4-4x^2+4=0 | | z-0.9z-2=6.5(z+5.6) | | y-8x=-2 | | x-2/3=-4/21 | | -4(x-1)+8x=4(x-6)-8 | | 4cos^2x-2=0 | | 46+3y-16=13y-12-4y | | 4x*2-225=0 | | .66(x-11)=4+x |

Equations solver categories