k^2+14k-88=0

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Solution for k^2+14k-88=0 equation:


Simplifying
k2 + 14k + -88 = 0

Reorder the terms:
-88 + 14k + k2 = 0

Solving
-88 + 14k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + 14k + 88 + k2 = 0 + 88

Reorder the terms:
-88 + 88 + 14k + k2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + 14k + k2 = 0 + 88
14k + k2 = 0 + 88

Combine like terms: 0 + 88 = 88
14k + k2 = 88

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

Add '49' to each side of the equation.
14k + 49 + k2 = 88 + 49

Reorder the terms:
49 + 14k + k2 = 88 + 49

Combine like terms: 88 + 49 = 137
49 + 14k + k2 = 137

Factor a perfect square on the left side:
(k + 7)(k + 7) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(k + 7) equal to 11.704699911 and -11.704699911.

Subproblem 1

k + 7 = 11.704699911 Simplifying k + 7 = 11.704699911 Reorder the terms: 7 + k = 11.704699911 Solving 7 + k = 11.704699911 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = 11.704699911 + -7 Combine like terms: 7 + -7 = 0 0 + k = 11.704699911 + -7 k = 11.704699911 + -7 Combine like terms: 11.704699911 + -7 = 4.704699911 k = 4.704699911 Simplifying k = 4.704699911

Subproblem 2

k + 7 = -11.704699911 Simplifying k + 7 = -11.704699911 Reorder the terms: 7 + k = -11.704699911 Solving 7 + k = -11.704699911 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = -11.704699911 + -7 Combine like terms: 7 + -7 = 0 0 + k = -11.704699911 + -7 k = -11.704699911 + -7 Combine like terms: -11.704699911 + -7 = -18.704699911 k = -18.704699911 Simplifying k = -18.704699911

Solution

The solution to the problem is based on the solutions from the subproblems. k = {4.704699911, -18.704699911}

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