3p^2+12p-37=0

Simple and best practice solution for 3p^2+12p-37=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 3p^2+12p-37=0 equation: 


Simplifying
3p2 + 12p + -37 = 0

Reorder the terms:
-37 + 12p + 3p2 = 0

Solving
-37 + 12p + 3p2 = 0

Solving for variable 'p'.

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

Divide each side by '3'.
-12.33333333 + 4p + p2 = 0

Move the constant term to the right:

Add '12.33333333' to each side of the equation.
-12.33333333 + 4p + 12.33333333 + p2 = 0 + 12.33333333

Reorder the terms:
-12.33333333 + 12.33333333 + 4p + p2 = 0 + 12.33333333

Combine like terms: -12.33333333 + 12.33333333 = 0.00000000
0.00000000 + 4p + p2 = 0 + 12.33333333
4p + p2 = 0 + 12.33333333

Combine like terms: 0 + 12.33333333 = 12.33333333
4p + p2 = 12.33333333

The p term is 4p.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4p + 4 + p2 = 12.33333333 + 4

Reorder the terms:
4 + 4p + p2 = 12.33333333 + 4

Combine like terms: 12.33333333 + 4 = 16.33333333
4 + 4p + p2 = 16.33333333

Factor a perfect square on the left side:
(p + 2)(p + 2) = 16.33333333

Calculate the square root of the right side: 4.041451884

Break this problem into two subproblems by setting 
(p + 2) equal to 4.041451884 and -4.041451884.


Subproblem 1
p + 2 = 4.041451884

Simplifying
p + 2 = 4.041451884

Reorder the terms:
2 + p = 4.041451884

Solving
2 + p = 4.041451884

Solving for variable 'p'.

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

Add '-2' to each side of the equation.
2 + -2 + p = 4.041451884 + -2

Combine like terms: 2 + -2 = 0
0 + p = 4.041451884 + -2
p = 4.041451884 + -2

Combine like terms: 4.041451884 + -2 = 2.041451884
p = 2.041451884

Simplifying
p = 2.041451884


Subproblem 2
p + 2 = -4.041451884

Simplifying
p + 2 = -4.041451884

Reorder the terms:
2 + p = -4.041451884

Solving
2 + p = -4.041451884

Solving for variable 'p'.

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

Add '-2' to each side of the equation.
2 + -2 + p = -4.041451884 + -2

Combine like terms: 2 + -2 = 0
0 + p = -4.041451884 + -2
p = -4.041451884 + -2

Combine like terms: -4.041451884 + -2 = -6.041451884
p = -6.041451884

Simplifying
p = -6.041451884


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.041451884, -6.041451884}

See similar equations:

| 100lnx-3x=100 | | a=1+ab | | h+2h=9 | | 5=-8a-7 | | 100lnx-x=100 | | 7-12=-X | | 3-4(-7)-6=1-2(-7)+10 | | -7w-20w+15w+8w=12 | | 4g-2g=14 | | -7(4n-9)=-32+8n | | 17c-15c=16 | | 18x^2=24x+6 | | 7-x=5x-5 | | at=c | | 7d-2d=5 | | 4n-n=9 | | -2h-7-8=31 | | 7/24=x/120 | | 7/24=m/120 | | 2/6-9i | | 31+3x-7=11 | | 4t=9w | | 1/(2х-10)=5 | | 1.2f=6 | | 3x+11=7-5 | | 11-3b=-1 | | Tg(x)+x=0 | | 13f=532 | | -2(4z-6)-3(3z+2)-6z= | | 8-x=14x-7 | | 5+-s=0 | | 32m^4+12m^3=4m^3 |

Equations solver categories