p^2=6p+19

Simple and best practice solution for p^2=6p+19 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=6p+19 equation:


Simplifying
p2 = 6p + 19

Reorder the terms:
p2 = 19 + 6p

Solving
p2 = 19 + 6p

Solving for variable 'p'.

Reorder the terms:
-19 + -6p + p2 = 19 + 6p + -19 + -6p

Reorder the terms:
-19 + -6p + p2 = 19 + -19 + 6p + -6p

Combine like terms: 19 + -19 = 0
-19 + -6p + p2 = 0 + 6p + -6p
-19 + -6p + p2 = 6p + -6p

Combine like terms: 6p + -6p = 0
-19 + -6p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -6p + 19 + p2 = 0 + 19

Reorder the terms:
-19 + 19 + -6p + p2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -6p + p2 = 0 + 19
-6p + p2 = 0 + 19

Combine like terms: 0 + 19 = 19
-6p + p2 = 19

The p term is -6p.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6p + 9 + p2 = 19 + 9

Reorder the terms:
9 + -6p + p2 = 19 + 9

Combine like terms: 19 + 9 = 28
9 + -6p + p2 = 28

Factor a perfect square on the left side:
(p + -3)(p + -3) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(p + -3) equal to 5.291502622 and -5.291502622.

Subproblem 1

p + -3 = 5.291502622 Simplifying p + -3 = 5.291502622 Reorder the terms: -3 + p = 5.291502622 Solving -3 + p = 5.291502622 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + p = 5.291502622 + 3 p = 5.291502622 + 3 Combine like terms: 5.291502622 + 3 = 8.291502622 p = 8.291502622 Simplifying p = 8.291502622

Subproblem 2

p + -3 = -5.291502622 Simplifying p + -3 = -5.291502622 Reorder the terms: -3 + p = -5.291502622 Solving -3 + p = -5.291502622 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + p = -5.291502622 + 3 p = -5.291502622 + 3 Combine like terms: -5.291502622 + 3 = -2.291502622 p = -2.291502622 Simplifying p = -2.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. p = {8.291502622, -2.291502622}

See similar equations:

| y=15c^2+25c^3 | | 144=(5+x)x | | 2X/5=3/2 | | 15/y=5 | | 8-(-5)-4(-70)= | | 2y+3=27 | | 3n^2+4n-3=n^2+3n | | 8x^2-16x+9=0 | | 98=c+52 | | x+24=89 | | 3y-4=2y+9 | | s-73=24 | | 7(x-3)=-2x+33 | | s-22=81 | | 12(x-4)+3x= | | 6a+2(a-4)=8 | | Sin1/2x | | 5p+2q=16 | | 2/3c:2 | | x+23=4x+5 | | x^3-11x^2+40x-48=0 | | 3/8=11/x | | x^3-11x^2-16x-48=0 | | 5/9d=9/101 | | 18yminus-17=7 | | -8v-5=-21http://www.thelearningodyssey.com/gatekeeper.aspx?INTERNAL=SESSION | | 0.2(d-6)+1.4d=1.6d-1.2 | | 5x+9=12x-12 | | an=1500-84n | | 2x-9=10x+15 | | Y+5=4(x+1) | | 7x=42+x |

Equations solver categories