p^2+22p=9

Simple and best practice solution for p^2+22p=9 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+22p=9 equation:


Simplifying
p2 + 22p = 9

Reorder the terms:
22p + p2 = 9

Solving
22p + p2 = 9

Solving for variable 'p'.

Reorder the terms:
-9 + 22p + p2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 22p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 22p + 9 + p2 = 0 + 9

Reorder the terms:
-9 + 9 + 22p + p2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 22p + p2 = 0 + 9
22p + p2 = 0 + 9

Combine like terms: 0 + 9 = 9
22p + p2 = 9

The p term is 22p.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22p + 121 + p2 = 9 + 121

Reorder the terms:
121 + 22p + p2 = 9 + 121

Combine like terms: 9 + 121 = 130
121 + 22p + p2 = 130

Factor a perfect square on the left side:
(p + 11)(p + 11) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(p + 11) equal to 11.401754251 and -11.401754251.

Subproblem 1

p + 11 = 11.401754251 Simplifying p + 11 = 11.401754251 Reorder the terms: 11 + p = 11.401754251 Solving 11 + p = 11.401754251 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = 11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + p = 11.401754251 + -11 p = 11.401754251 + -11 Combine like terms: 11.401754251 + -11 = 0.401754251 p = 0.401754251 Simplifying p = 0.401754251

Subproblem 2

p + 11 = -11.401754251 Simplifying p + 11 = -11.401754251 Reorder the terms: 11 + p = -11.401754251 Solving 11 + p = -11.401754251 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = -11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + p = -11.401754251 + -11 p = -11.401754251 + -11 Combine like terms: -11.401754251 + -11 = -22.401754251 p = -22.401754251 Simplifying p = -22.401754251

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.401754251, -22.401754251}

See similar equations:

| 20x+30=10x | | 0.07x=2.38 | | (2,-1);m=5/4 | | y-5=6(x+7) | | X-6=2.87 | | 70=7(m+3.3) | | -6y=3.72 | | y=9-(x-3) | | 3=3/4n-18 | | (4y^3/8z^6)^5 | | 6y-15y-19=-19 | | X+2.9=8.6 | | y-2=-4(x-10) | | (2x-3)+(7x+4)= | | 10(6.6)+15= | | y-5=-9(x+1) | | 17-3x=2+7x | | 2x-8yi=-2+4yi | | 5(x-2)=16-x | | y-3=16(x-6) | | 104=12x+w | | -1/105m=8 | | 40-73d-80-9d+2+6d= | | y+1=-10(x+1) | | -2(y-w)-(w-6y)= | | -8045=5k | | 19=13 | | N-15=-3 | | x^2+9-5x=0 | | y+3=5(x-4) | | ln(6x+3)-ln(9x)=5 | | 1/2=x/17 |

Equations solver categories