13y^2+216y-36=0

Simple and best practice solution for 13y^2+216y-36=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 13y^2+216y-36=0 equation:


Simplifying
13y2 + 216y + -36 = 0

Reorder the terms:
-36 + 216y + 13y2 = 0

Solving
-36 + 216y + 13y2 = 0

Solving for variable 'y'.

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

Divide each side by '13'.
-2.769230769 + 16.61538462y + y2 = 0

Move the constant term to the right:

Add '2.769230769' to each side of the equation.
-2.769230769 + 16.61538462y + 2.769230769 + y2 = 0 + 2.769230769

Reorder the terms:
-2.769230769 + 2.769230769 + 16.61538462y + y2 = 0 + 2.769230769

Combine like terms: -2.769230769 + 2.769230769 = 0.000000000
0.000000000 + 16.61538462y + y2 = 0 + 2.769230769
16.61538462y + y2 = 0 + 2.769230769

Combine like terms: 0 + 2.769230769 = 2.769230769
16.61538462y + y2 = 2.769230769

The y term is 16.61538462y.  Take half its coefficient (8.30769231).
Square it (69.01775152) and add it to both sides.

Add '69.01775152' to each side of the equation.
16.61538462y + 69.01775152 + y2 = 2.769230769 + 69.01775152

Reorder the terms:
69.01775152 + 16.61538462y + y2 = 2.769230769 + 69.01775152

Combine like terms: 2.769230769 + 69.01775152 = 71.786982289
69.01775152 + 16.61538462y + y2 = 71.786982289

Factor a perfect square on the left side:
(y + 8.30769231)(y + 8.30769231) = 71.786982289

Calculate the square root of the right side: 8.472719887

Break this problem into two subproblems by setting 
(y + 8.30769231) equal to 8.472719887 and -8.472719887.

Subproblem 1

y + 8.30769231 = 8.472719887 Simplifying y + 8.30769231 = 8.472719887 Reorder the terms: 8.30769231 + y = 8.472719887 Solving 8.30769231 + y = 8.472719887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.30769231' to each side of the equation. 8.30769231 + -8.30769231 + y = 8.472719887 + -8.30769231 Combine like terms: 8.30769231 + -8.30769231 = 0.00000000 0.00000000 + y = 8.472719887 + -8.30769231 y = 8.472719887 + -8.30769231 Combine like terms: 8.472719887 + -8.30769231 = 0.165027577 y = 0.165027577 Simplifying y = 0.165027577

Subproblem 2

y + 8.30769231 = -8.472719887 Simplifying y + 8.30769231 = -8.472719887 Reorder the terms: 8.30769231 + y = -8.472719887 Solving 8.30769231 + y = -8.472719887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.30769231' to each side of the equation. 8.30769231 + -8.30769231 + y = -8.472719887 + -8.30769231 Combine like terms: 8.30769231 + -8.30769231 = 0.00000000 0.00000000 + y = -8.472719887 + -8.30769231 y = -8.472719887 + -8.30769231 Combine like terms: -8.472719887 + -8.30769231 = -16.780412197 y = -16.780412197 Simplifying y = -16.780412197

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.165027577, -16.780412197}

See similar equations:

| 2.5+.075P=1P | | y^2-11y+32=2 | | 3(2n-1)=(2n+6)+1 | | (4a-5)=(2a-3) | | -9x-4=7x-16 | | y+5=0.2y+4.4 | | x+6-340+64=570 | | 10n=18n | | X+x^2-58=128 | | 8(2)-2x=46 | | 0.9x-2.9=0.7 | | 5(-w-2z)-6(-7z+5w)= | | 2x-5=+7 | | 22.3-3u=3.1 | | 42x-13x-30x=46 | | 8x=4x+44 | | (5k-25)-(6k+2)+7= | | -7x-4=-6x-8 | | 0.50t+3=1 | | 5y+5z=15 | | 5x+2=7+4x | | 6+4x=6x-8x-2 | | -4w-6(4x-4w)+3x= | | 3a+b-20=a-4b+42 | | 5(7x+2)-3=35x+7 | | -.5x+4=-2 | | 7w-(-z+6w)+5z= | | 150+(4n)=10n | | 4y-6+y+37=5y+40-3y | | 3x+6x-6x-2x+2=23 | | x+20=90-x | | 3x^2+18x=(-30) |

Equations solver categories