-4p^2-120p-196=0

Simple and best practice solution for -4p^2-120p-196=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 -4p^2-120p-196=0 equation: 


Simplifying
-4p2 + -120p + -196 = 0

Reorder the terms:
-196 + -120p + -4p2 = 0

Solving
-196 + -120p + -4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(49 + 30p + p2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(49 + 30p + p2)' equal to zero and attempt to solve:

Simplifying
49 + 30p + p2 = 0

Solving
49 + 30p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 30p + -49 + p2 = 0 + -49

Reorder the terms:
49 + -49 + 30p + p2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 30p + p2 = 0 + -49
30p + p2 = 0 + -49

Combine like terms: 0 + -49 = -49
30p + p2 = -49

The p term is 30p.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30p + 225 + p2 = -49 + 225

Reorder the terms:
225 + 30p + p2 = -49 + 225

Combine like terms: -49 + 225 = 176
225 + 30p + p2 = 176

Factor a perfect square on the left side:
(p + 15)(p + 15) = 176

Calculate the square root of the right side: 13.266499161

Break this problem into two subproblems by setting 
(p + 15) equal to 13.266499161 and -13.266499161.


Subproblem 1
p + 15 = 13.266499161

Simplifying
p + 15 = 13.266499161

Reorder the terms:
15 + p = 13.266499161

Solving
15 + p = 13.266499161

Solving for variable 'p'.

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

Add '-15' to each side of the equation.
15 + -15 + p = 13.266499161 + -15

Combine like terms: 15 + -15 = 0
0 + p = 13.266499161 + -15
p = 13.266499161 + -15

Combine like terms: 13.266499161 + -15 = -1.733500839
p = -1.733500839

Simplifying
p = -1.733500839


Subproblem 2
p + 15 = -13.266499161

Simplifying
p + 15 = -13.266499161

Reorder the terms:
15 + p = -13.266499161

Solving
15 + p = -13.266499161

Solving for variable 'p'.

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

Add '-15' to each side of the equation.
15 + -15 + p = -13.266499161 + -15

Combine like terms: 15 + -15 = 0
0 + p = -13.266499161 + -15
p = -13.266499161 + -15

Combine like terms: -13.266499161 + -15 = -28.266499161
p = -28.266499161

Simplifying
p = -28.266499161


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-1.733500839, -28.266499161}
Solution
p = {-1.733500839, -28.266499161}

See similar equations:

| d^2+8d=9 | | -2z^2-12z=-26 | | 2650000/100-50 | | r^2+20r-47=0 | | 4=-1y | | 7x-12x= | | -4w^2-64w=-12 | | 2c+31=c+6 | | 1.25(2000)+800/2000 | | 1/6(5x-6)=4 | | h^2-16h-9=0 | | 1.25(500)+800/500 | | 40x^2-25x=0 | | d^2+24d+7=0 | | j^2+2j=45 | | g^2+28g=-29 | | 1/4(1/3) | | -4r^2+64r-76=0 | | t^2+14t=-19 | | f^2+4f-39=0 | | u^2+6u=37 | | 3v+9=27 | | 30=r+2/3 | | t^2-24t=1 | | 2d^2+48d=98 | | 5x+2x+10=80 | | y-b/x | | u^2-18u=-29 | | -3x+36=9 | | x+2/3=1+x/3 | | 5x+7+3x+8=127+6x-14 | | y^2+6y=-7 |

Equations solver categories