16p^2-6=6p-7+10p^2

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Solution for 16p^2-6=6p-7+10p^2 equation:


Simplifying
16p2 + -6 = 6p + -7 + 10p2

Reorder the terms:
-6 + 16p2 = 6p + -7 + 10p2

Reorder the terms:
-6 + 16p2 = -7 + 6p + 10p2

Solving
-6 + 16p2 = -7 + 6p + 10p2

Solving for variable 'p'.

Reorder the terms:
-6 + 7 + -6p + 16p2 + -10p2 = -7 + 6p + 10p2 + 7 + -6p + -10p2

Combine like terms: -6 + 7 = 1
1 + -6p + 16p2 + -10p2 = -7 + 6p + 10p2 + 7 + -6p + -10p2

Combine like terms: 16p2 + -10p2 = 6p2
1 + -6p + 6p2 = -7 + 6p + 10p2 + 7 + -6p + -10p2

Reorder the terms:
1 + -6p + 6p2 = -7 + 7 + 6p + -6p + 10p2 + -10p2

Combine like terms: -7 + 7 = 0
1 + -6p + 6p2 = 0 + 6p + -6p + 10p2 + -10p2
1 + -6p + 6p2 = 6p + -6p + 10p2 + -10p2

Combine like terms: 6p + -6p = 0
1 + -6p + 6p2 = 0 + 10p2 + -10p2
1 + -6p + 6p2 = 10p2 + -10p2

Combine like terms: 10p2 + -10p2 = 0
1 + -6p + 6p2 = 0

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

Divide each side by '6'.
0.1666666667 + -1p + p2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -1p + -0.1666666667 + p2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -1p + p2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -1p + p2 = 0 + -0.1666666667
-1p + p2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-1p + p2 = -0.1666666667

The p term is -1p.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1p + 0.25 + p2 = -0.1666666667 + 0.25

Reorder the terms:
0.25 + -1p + p2 = -0.1666666667 + 0.25

Combine like terms: -0.1666666667 + 0.25 = 0.0833333333
0.25 + -1p + p2 = 0.0833333333

Factor a perfect square on the left side:
(p + -0.5)(p + -0.5) = 0.0833333333

Calculate the square root of the right side: 0.288675135

Break this problem into two subproblems by setting 
(p + -0.5) equal to 0.288675135 and -0.288675135.

Subproblem 1

p + -0.5 = 0.288675135 Simplifying p + -0.5 = 0.288675135 Reorder the terms: -0.5 + p = 0.288675135 Solving -0.5 + p = 0.288675135 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 0.288675135 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 0.288675135 + 0.5 p = 0.288675135 + 0.5 Combine like terms: 0.288675135 + 0.5 = 0.788675135 p = 0.788675135 Simplifying p = 0.788675135

Subproblem 2

p + -0.5 = -0.288675135 Simplifying p + -0.5 = -0.288675135 Reorder the terms: -0.5 + p = -0.288675135 Solving -0.5 + p = -0.288675135 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -0.288675135 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -0.288675135 + 0.5 p = -0.288675135 + 0.5 Combine like terms: -0.288675135 + 0.5 = 0.211324865 p = 0.211324865 Simplifying p = 0.211324865

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.788675135, 0.211324865}

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