3(p-7)4p+11=

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Solution for 3(p-7)4p+11= equation:


Simplifying
3(p + -7) * 4p + 11 = 0

Reorder the terms:
3(-7 + p) * 4p + 11 = 0

Reorder the terms for easier multiplication:
3 * 4p(-7 + p) + 11 = 0

Multiply 3 * 4
12p(-7 + p) + 11 = 0
(-7 * 12p + p * 12p) + 11 = 0
(-84p + 12p2) + 11 = 0

Reorder the terms:
11 + -84p + 12p2 = 0

Solving
11 + -84p + 12p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
0.9166666667 + -7p + p2 = 0

Move the constant term to the right:

Add '-0.9166666667' to each side of the equation.
0.9166666667 + -7p + -0.9166666667 + p2 = 0 + -0.9166666667

Reorder the terms:
0.9166666667 + -0.9166666667 + -7p + p2 = 0 + -0.9166666667

Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000
0.0000000000 + -7p + p2 = 0 + -0.9166666667
-7p + p2 = 0 + -0.9166666667

Combine like terms: 0 + -0.9166666667 = -0.9166666667
-7p + p2 = -0.9166666667

The p term is -7p.  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.
-7p + 12.25 + p2 = -0.9166666667 + 12.25

Reorder the terms:
12.25 + -7p + p2 = -0.9166666667 + 12.25

Combine like terms: -0.9166666667 + 12.25 = 11.3333333333
12.25 + -7p + p2 = 11.3333333333

Factor a perfect square on the left side:
(p + -3.5)(p + -3.5) = 11.3333333333

Calculate the square root of the right side: 3.366501646

Break this problem into two subproblems by setting 
(p + -3.5) equal to 3.366501646 and -3.366501646.

Subproblem 1

p + -3.5 = 3.366501646 Simplifying p + -3.5 = 3.366501646 Reorder the terms: -3.5 + p = 3.366501646 Solving -3.5 + p = 3.366501646 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 + p = 3.366501646 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = 3.366501646 + 3.5 p = 3.366501646 + 3.5 Combine like terms: 3.366501646 + 3.5 = 6.866501646 p = 6.866501646 Simplifying p = 6.866501646

Subproblem 2

p + -3.5 = -3.366501646 Simplifying p + -3.5 = -3.366501646 Reorder the terms: -3.5 + p = -3.366501646 Solving -3.5 + p = -3.366501646 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 + p = -3.366501646 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + p = -3.366501646 + 3.5 p = -3.366501646 + 3.5 Combine like terms: -3.366501646 + 3.5 = 0.133498354 p = 0.133498354 Simplifying p = 0.133498354

Solution

The solution to the problem is based on the solutions from the subproblems. p = {6.866501646, 0.133498354}

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