p^2(p^2-4)=3p^2-11

Simple and best practice solution for p^2(p^2-4)=3p^2-11 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(p^2-4)=3p^2-11 equation: 


Simplifying
p2(p2 + -4) = 3p2 + -11

Reorder the terms:
p2(-4 + p2) = 3p2 + -11
(-4 * p2 + p2 * p2) = 3p2 + -11
(-4p2 + p4) = 3p2 + -11

Reorder the terms:
-4p2 + p4 = -11 + 3p2

Solving
-4p2 + p4 = -11 + 3p2

Solving for variable 'p'.

Reorder the terms:
11 + -4p2 + -3p2 + p4 = -11 + 3p2 + 11 + -3p2

Combine like terms: -4p2 + -3p2 = -7p2
11 + -7p2 + p4 = -11 + 3p2 + 11 + -3p2

Reorder the terms:
11 + -7p2 + p4 = -11 + 11 + 3p2 + -3p2

Combine like terms: -11 + 11 = 0
11 + -7p2 + p4 = 0 + 3p2 + -3p2
11 + -7p2 + p4 = 3p2 + -3p2

Combine like terms: 3p2 + -3p2 = 0
11 + -7p2 + p4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -7p2 + -11 + p4 = 0 + -11

Reorder the terms:
11 + -11 + -7p2 + p4 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -7p2 + p4 = 0 + -11
-7p2 + p4 = 0 + -11

Combine like terms: 0 + -11 = -11
-7p2 + p4 = -11

The p term is -7p2.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7p2 + 12.25 + p4 = -11 + 12.25

Reorder the terms:
12.25 + -7p2 + p4 = -11 + 12.25

Combine like terms: -11 + 12.25 = 1.25
12.25 + -7p2 + p4 = 1.25

Factor a perfect square on the left side:
(p2 + -3.5)(p2 + -3.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(p2 + -3.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
p2 + -3.5 = 1.118033989

Simplifying
p2 + -3.5 = 1.118033989

Reorder the terms:
-3.5 + p2 = 1.118033989

Solving
-3.5 + p2 = 1.118033989

Solving for variable 'p'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + p2 = 1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p2 = 1.118033989 + 3.5
p2 = 1.118033989 + 3.5

Combine like terms: 1.118033989 + 3.5 = 4.618033989
p2 = 4.618033989

Simplifying
p2 = 4.618033989

Take the square root of each side:
p = {-2.148961142, 2.148961142}


Subproblem 2
p2 + -3.5 = -1.118033989

Simplifying
p2 + -3.5 = -1.118033989

Reorder the terms:
-3.5 + p2 = -1.118033989

Solving
-3.5 + p2 = -1.118033989

Solving for variable 'p'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + p2 = -1.118033989 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p2 = -1.118033989 + 3.5
p2 = -1.118033989 + 3.5

Combine like terms: -1.118033989 + 3.5 = 2.381966011
p2 = 2.381966011

Simplifying
p2 = 2.381966011

Take the square root of each side:
p = {-1.543361918, 1.543361918}


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-2.148961142, 2.148961142, -1.543361918, 1.543361918}

See similar equations:

| -8-7x=-8 | | -10+2x+3(5-x)=2(4x-8) | | -8-7=-8 | | 60-2p=25+p | | 0.75m+3=6 | | -7y-3+6y+6=5 | | 6.8t-10-3.2=3t-1 | | 2y(y+4)-10=0 | | 75r^2-27=0 | | 3+y=-6 | | -x+(x+2)=2 | | 12t-4t=96 | | 15n+85=c | | x+(x+2)=2 | | 17404+62900x=1201.98 | | 2t+7=6 | | 2x+10-5x=7x-63 | | 0.5+7=6 | | 2(15)= | | y-2=1(x+9) | | 8z+2=2 | | 0.5d-5=2 | | 8x+4=4(x-7) | | 6(-6x-8)=9x | | 3/4(5+x)=10 | | -4(2x+4)=-18x+8 | | -6-2p=-3(1-3p)-3 | | 4(3x-4)=52 | | 10=10x(9x-10) | | 2+3x=5+3x | | 4(-8x-2)+4x=-5 | | 2r-(5-r)=14+2r |

Equations solver categories