3p^2-16p+3=0

Simple and best practice solution for 3p^2-16p+3=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^2-16p+3=0 equation: 


Simplifying
3p2 + -16p + 3 = 0

Reorder the terms:
3 + -16p + 3p2 = 0

Solving
3 + -16p + 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'.
1 + -5.333333333p + p2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -5.333333333p + -1 + p2 = 0 + -1

Reorder the terms:
1 + -1 + -5.333333333p + p2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5.333333333p + p2 = 0 + -1
-5.333333333p + p2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5.333333333p + p2 = -1

The p term is -5.333333333p.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333p + 7.111111113 + p2 = -1 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333p + p2 = -1 + 7.111111113

Combine like terms: -1 + 7.111111113 = 6.111111113
7.111111113 + -5.333333333p + p2 = 6.111111113

Factor a perfect square on the left side:
(p + -2.666666667)(p + -2.666666667) = 6.111111113

Calculate the square root of the right side: 2.472066163

Break this problem into two subproblems by setting 
(p + -2.666666667) equal to 2.472066163 and -2.472066163.


Subproblem 1
p + -2.666666667 = 2.472066163

Simplifying
p + -2.666666667 = 2.472066163

Reorder the terms:
-2.666666667 + p = 2.472066163

Solving
-2.666666667 + p = 2.472066163

Solving for variable 'p'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + p = 2.472066163 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + p = 2.472066163 + 2.666666667
p = 2.472066163 + 2.666666667

Combine like terms: 2.472066163 + 2.666666667 = 5.13873283
p = 5.13873283

Simplifying
p = 5.13873283


Subproblem 2
p + -2.666666667 = -2.472066163

Simplifying
p + -2.666666667 = -2.472066163

Reorder the terms:
-2.666666667 + p = -2.472066163

Solving
-2.666666667 + p = -2.472066163

Solving for variable 'p'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + p = -2.472066163 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + p = -2.472066163 + 2.666666667
p = -2.472066163 + 2.666666667

Combine like terms: -2.472066163 + 2.666666667 = 0.194600504
p = 0.194600504

Simplifying
p = 0.194600504


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.13873283, 0.194600504}

See similar equations:

| 9t-25=-25+7t | | (7t)+(10t-15)=180 | | 5t(9-t)=0 | | 6x-6x=2+4-6 | | 6-5a=7+2a-6a | | 2=-16t^2+14t+6 | | -n+3=-n-5 | | 36.71=-26(X)+61.8 | | 10x^3-39x^2+23x+30=0 | | 16t-8t-15=0 | | 23.85=-26(X)+61.8 | | 3u^5-14u^3-80u=0 | | 8x^5-76x^3+96x=0 | | 1+3x-6x=-20 | | 20m^5-96m^3+64m=0 | | -16x+13x=-24 | | 3m^3-33m^2+84m=0 | | 3x^2-8=12 | | 4g-5g+9=0 | | 3x+7+x-4-2x=8 | | 2(5-5x^2)=5 | | 4+2x=3+5x | | (11-5) = 3x+10 | | -7x-10+6x=22 | | -5-2x=6-7x | | 3u^5+25u^3+8u=0 | | -7-10+6=22 | | 4a+3=-b+9 | | -7x-10-6x=22 | | 30w^2(x^6)(y^9)=24w^5(x^8) | | 30w^2(x^6)(y^9)-24w^5(x^8)=1 | | y=-2x^2+12x-11 |

Equations solver categories