p^2+14p-70=3

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Solution for p^2+14p-70=3 equation:


Simplifying
p2 + 14p + -70 = 3

Reorder the terms:
-70 + 14p + p2 = 3

Solving
-70 + 14p + p2 = 3

Solving for variable 'p'.

Reorder the terms:
-70 + -3 + 14p + p2 = 3 + -3

Combine like terms: -70 + -3 = -73
-73 + 14p + p2 = 3 + -3

Combine like terms: 3 + -3 = 0
-73 + 14p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + 14p + 73 + p2 = 0 + 73

Reorder the terms:
-73 + 73 + 14p + p2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + 14p + p2 = 0 + 73
14p + p2 = 0 + 73

Combine like terms: 0 + 73 = 73
14p + p2 = 73

The p term is 14p.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14p + 49 + p2 = 73 + 49

Reorder the terms:
49 + 14p + p2 = 73 + 49

Combine like terms: 73 + 49 = 122
49 + 14p + p2 = 122

Factor a perfect square on the left side:
(p + 7)(p + 7) = 122

Calculate the square root of the right side: 11.045361017

Break this problem into two subproblems by setting 
(p + 7) equal to 11.045361017 and -11.045361017.

Subproblem 1

p + 7 = 11.045361017 Simplifying p + 7 = 11.045361017 Reorder the terms: 7 + p = 11.045361017 Solving 7 + p = 11.045361017 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = 11.045361017 + -7 Combine like terms: 7 + -7 = 0 0 + p = 11.045361017 + -7 p = 11.045361017 + -7 Combine like terms: 11.045361017 + -7 = 4.045361017 p = 4.045361017 Simplifying p = 4.045361017

Subproblem 2

p + 7 = -11.045361017 Simplifying p + 7 = -11.045361017 Reorder the terms: 7 + p = -11.045361017 Solving 7 + p = -11.045361017 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = -11.045361017 + -7 Combine like terms: 7 + -7 = 0 0 + p = -11.045361017 + -7 p = -11.045361017 + -7 Combine like terms: -11.045361017 + -7 = -18.045361017 p = -18.045361017 Simplifying p = -18.045361017

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.045361017, -18.045361017}

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