-7p(p+8)=21

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Solution for -7p(p+8)=21 equation: 


Simplifying
-7p(p + 8) = 21

Reorder the terms:
-7p(8 + p) = 21
(8 * -7p + p * -7p) = 21
(-56p + -7p2) = 21

Solving
-56p + -7p2 = 21

Solving for variable 'p'.

Reorder the terms:
-21 + -56p + -7p2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -56p + -7p2 = 0

Factor out the Greatest Common Factor (GCF), '-7'.
-7(3 + 8p + p2) = 0

Ignore the factor -7.

Subproblem 1
Set the factor '(3 + 8p + p2)' equal to zero and attempt to solve:

Simplifying
3 + 8p + p2 = 0

Solving
3 + 8p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 8p + -3 + p2 = 0 + -3

Reorder the terms:
3 + -3 + 8p + p2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8p + p2 = 0 + -3
8p + p2 = 0 + -3

Combine like terms: 0 + -3 = -3
8p + p2 = -3

The p term is 8p.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8p + 16 + p2 = -3 + 16

Reorder the terms:
16 + 8p + p2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + 8p + p2 = 13

Factor a perfect square on the left side:
(p + 4)(p + 4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(p + 4) equal to 3.605551275 and -3.605551275.


Subproblem 1
p + 4 = 3.605551275

Simplifying
p + 4 = 3.605551275

Reorder the terms:
4 + p = 3.605551275

Solving
4 + p = 3.605551275

Solving for variable 'p'.

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

Add '-4' to each side of the equation.
4 + -4 + p = 3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + p = 3.605551275 + -4
p = 3.605551275 + -4

Combine like terms: 3.605551275 + -4 = -0.394448725
p = -0.394448725

Simplifying
p = -0.394448725


Subproblem 2
p + 4 = -3.605551275

Simplifying
p + 4 = -3.605551275

Reorder the terms:
4 + p = -3.605551275

Solving
4 + p = -3.605551275

Solving for variable 'p'.

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

Add '-4' to each side of the equation.
4 + -4 + p = -3.605551275 + -4

Combine like terms: 4 + -4 = 0
0 + p = -3.605551275 + -4
p = -3.605551275 + -4

Combine like terms: -3.605551275 + -4 = -7.605551275
p = -7.605551275

Simplifying
p = -7.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.394448725, -7.605551275}
Solution
p = {-0.394448725, -7.605551275}

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