3y^2+31y=36

Simple and best practice solution for 3y^2+31y=36 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 3y^2+31y=36 equation:


Simplifying
3y2 + 31y = 36

Reorder the terms:
31y + 3y2 = 36

Solving
31y + 3y2 = 36

Solving for variable 'y'.

Reorder the terms:
-36 + 31y + 3y2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 31y + 3y2 = 0

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

Divide each side by '3'.
-12 + 10.33333333y + y2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 10.33333333y + 12 + y2 = 0 + 12

Reorder the terms:
-12 + 12 + 10.33333333y + y2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 10.33333333y + y2 = 0 + 12
10.33333333y + y2 = 0 + 12

Combine like terms: 0 + 12 = 12
10.33333333y + y2 = 12

The y term is 10.33333333y.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333y + 26.69444443 + y2 = 12 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333y + y2 = 12 + 26.69444443

Combine like terms: 12 + 26.69444443 = 38.69444443
26.69444443 + 10.33333333y + y2 = 38.69444443

Factor a perfect square on the left side:
(y + 5.166666665)(y + 5.166666665) = 38.69444443

Calculate the square root of the right side: 6.220485868

Break this problem into two subproblems by setting 
(y + 5.166666665) equal to 6.220485868 and -6.220485868.

Subproblem 1

y + 5.166666665 = 6.220485868 Simplifying y + 5.166666665 = 6.220485868 Reorder the terms: 5.166666665 + y = 6.220485868 Solving 5.166666665 + y = 6.220485868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + y = 6.220485868 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + y = 6.220485868 + -5.166666665 y = 6.220485868 + -5.166666665 Combine like terms: 6.220485868 + -5.166666665 = 1.053819203 y = 1.053819203 Simplifying y = 1.053819203

Subproblem 2

y + 5.166666665 = -6.220485868 Simplifying y + 5.166666665 = -6.220485868 Reorder the terms: 5.166666665 + y = -6.220485868 Solving 5.166666665 + y = -6.220485868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + y = -6.220485868 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + y = -6.220485868 + -5.166666665 y = -6.220485868 + -5.166666665 Combine like terms: -6.220485868 + -5.166666665 = -11.387152533 y = -11.387152533 Simplifying y = -11.387152533

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.053819203, -11.387152533}

See similar equations:

| y=540-9x | | d/2+d/6 | | 36+5x-x^2=0 | | -7x+6/7+8/7=-7x/4 | | 28+3x-x^2=0 | | 35-2x-x^2=0 | | 2x+1=5x-14 | | 180=12x+4y | | 54-3x-x^2=0 | | 180=27x+y | | 11x+13n=209 | | 3x+x^2=32 | | 25x^2+40x+9=0 | | 9x^2-p^2=0 | | 2.5x+1.5y=2200 | | x+6/x+1-2=0 | | 0.12x+0.3(x-4)=0.01(2x-3) | | 0.8z+2.7=0.1z+9 | | 11-7x-7-14x=7 | | 8/5(x-8)=1/2 | | 32+9/5(77.35-273.15)=f | | 10x+5=3x-15 | | (7.3x)(x+2)=4 | | x/5-5/4=x/10-1/20 | | 3(3x-7)=24 | | r+3/5=-7/10 | | 1/7*7/29 | | 9x-3(x-2)=9x+15-2x | | 4x-6x=x^2 | | -10+2*(3*x+1)=4(5-2*x) | | -9x-13=-4+32 | | 80v^2+44v-12= |

Equations solver categories