p^2-3p+1=0

Simple and best practice solution for p^2-3p+1=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 p^2-3p+1=0 equation:


Simplifying
p2 + -3p + 1 = 0

Reorder the terms:
1 + -3p + p2 = 0

Solving
1 + -3p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3p + -1 + p2 = 0 + -1

Reorder the terms:
1 + -1 + -3p + p2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3p + p2 = 0 + -1
-3p + p2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3p + p2 = -1

The p term is -3p.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3p + 2.25 + p2 = -1 + 2.25

Reorder the terms:
2.25 + -3p + p2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3p + p2 = 1.25

Factor a perfect square on the left side:
(p + -1.5)(p + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(p + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

p + -1.5 = 1.118033989 Simplifying p + -1.5 = 1.118033989 Reorder the terms: -1.5 + p = 1.118033989 Solving -1.5 + p = 1.118033989 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 1.118033989 + 1.5 p = 1.118033989 + 1.5 Combine like terms: 1.118033989 + 1.5 = 2.618033989 p = 2.618033989 Simplifying p = 2.618033989

Subproblem 2

p + -1.5 = -1.118033989 Simplifying p + -1.5 = -1.118033989 Reorder the terms: -1.5 + p = -1.118033989 Solving -1.5 + p = -1.118033989 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -1.118033989 + 1.5 p = -1.118033989 + 1.5 Combine like terms: -1.118033989 + 1.5 = 0.381966011 p = 0.381966011 Simplifying p = 0.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. p = {2.618033989, 0.381966011}

See similar equations:

| 78c^2+42c=0 | | (s+12)+s=390 | | 3(x-5)-(2x+1)=3-x | | 16d+8c=10000 | | x^2+.41x-.095=0 | | x^2+56x-1920=0 | | 5a^2=11a+12 | | x^2+2x+55=90 | | 7a^3=63a | | -x^2-x-1=0 | | 9(4x-3)=3(12x+6) | | 9(4x-3)=3(12+6) | | 3m+2(m+2)=20-(2m-5) | | 6(t-3)+6t=4(3t+3)-11 | | -(3y+1)-(-2y-4)=0 | | 17(t-5)+4t=7(3t+3)-12 | | 9+19n-4=5n+53-2n | | 3+11s-1=4s+56-2s | | -(3y+1)-(-2y-6)=0 | | y-12=-5 | | x-8.9=-6.3 | | 4+x=290 | | h=16t^2+32t+1008 | | y=-5(4)-2 | | 2y=-x+3 | | 9k-4k-8k=-15 | | 1.6q-3.5-4.5q=3.9q-1.2 | | y=-5(-2)-2 | | -3(3b+3)+(10b-9)=0 | | 10y=-5x+15 | | 4x^2+25-9=0 | | -9=4w-3 |

Equations solver categories