3p^2-11p+3=0

Simple and best practice solution for 3p^2-11p+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^2-11p+3=0 equation:


Simplifying
3p2 + -11p + 3 = 0

Reorder the terms:
3 + -11p + 3p2 = 0

Solving
3 + -11p + 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 + -3.666666667p + p2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.666666667p + -1 + p2 = 0 + -1

Reorder the terms:
1 + -1 + -3.666666667p + p2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.666666667p + p2 = 0 + -1
-3.666666667p + p2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.666666667p + p2 = -1

The p term is -3.666666667p.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667p + 3.361111114 + p2 = -1 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667p + p2 = -1 + 3.361111114

Combine like terms: -1 + 3.361111114 = 2.361111114
3.361111114 + -3.666666667p + p2 = 2.361111114

Factor a perfect square on the left side:
(p + -1.833333334)(p + -1.833333334) = 2.361111114

Calculate the square root of the right side: 1.536590744

Break this problem into two subproblems by setting 
(p + -1.833333334) equal to 1.536590744 and -1.536590744.

Subproblem 1

p + -1.833333334 = 1.536590744 Simplifying p + -1.833333334 = 1.536590744 Reorder the terms: -1.833333334 + p = 1.536590744 Solving -1.833333334 + p = 1.536590744 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + p = 1.536590744 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + p = 1.536590744 + 1.833333334 p = 1.536590744 + 1.833333334 Combine like terms: 1.536590744 + 1.833333334 = 3.369924078 p = 3.369924078 Simplifying p = 3.369924078

Subproblem 2

p + -1.833333334 = -1.536590744 Simplifying p + -1.833333334 = -1.536590744 Reorder the terms: -1.833333334 + p = -1.536590744 Solving -1.833333334 + p = -1.536590744 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + p = -1.536590744 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + p = -1.536590744 + 1.833333334 p = -1.536590744 + 1.833333334 Combine like terms: -1.536590744 + 1.833333334 = 0.29674259 p = 0.29674259 Simplifying p = 0.29674259

Solution

The solution to the problem is based on the solutions from the subproblems. p = {3.369924078, 0.29674259}

See similar equations:

| 2m+wr=r-7f | | 6-7d(5d+6)=5 | | 12(5+2y)=4y-6(6-9y) | | 4x^2=2x-3 | | 8x+21+7x-6=180 | | 15y-4=13y+7 | | -6y=4y-20 | | 4x-7/3=2x | | r^3+3r^2+28r+26=0 | | 85=175t+-16t^2 | | x/2-14=22 | | 10+b/18=1 | | h^2-5h+8=0 | | -42x+5=-16 | | h=175t+-16t^2 | | h=175t-16t^2 | | 4x-2(x-2)=2(x+1) | | (3-x)/2=(1+2x)/3 | | -4=b/2-9 | | 5x^2+13x-6=-6-4x | | -113=1+6x | | 3x/5=4/7 | | -5n-4=-9 | | -17x^17y^5/68x^4y^5 | | 6-1/6=4x-3 | | 6-13/18=4x-3 | | -3+2y=5 | | 8.8-22=2.3+75.5 | | 3/49z | | 4/2z-3 | | 1+2y=5 | | x(2x+13)=24 |

Equations solver categories