k^2+14k-78=-10

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Solution for k^2+14k-78=-10 equation:


Simplifying
k2 + 14k + -78 = -10

Reorder the terms:
-78 + 14k + k2 = -10

Solving
-78 + 14k + k2 = -10

Solving for variable 'k'.

Reorder the terms:
-78 + 10 + 14k + k2 = -10 + 10

Combine like terms: -78 + 10 = -68
-68 + 14k + k2 = -10 + 10

Combine like terms: -10 + 10 = 0
-68 + 14k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 14k + 68 + k2 = 0 + 68

Reorder the terms:
-68 + 68 + 14k + k2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 14k + k2 = 0 + 68
14k + k2 = 0 + 68

Combine like terms: 0 + 68 = 68
14k + k2 = 68

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 = 68 + 49

Reorder the terms:
49 + 14k + k2 = 68 + 49

Combine like terms: 68 + 49 = 117
49 + 14k + k2 = 117

Factor a perfect square on the left side:
(k + 7)(k + 7) = 117

Calculate the square root of the right side: 10.816653826

Break this problem into two subproblems by setting 
(k + 7) equal to 10.816653826 and -10.816653826.

Subproblem 1

k + 7 = 10.816653826 Simplifying k + 7 = 10.816653826 Reorder the terms: 7 + k = 10.816653826 Solving 7 + k = 10.816653826 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 = 10.816653826 + -7 Combine like terms: 7 + -7 = 0 0 + k = 10.816653826 + -7 k = 10.816653826 + -7 Combine like terms: 10.816653826 + -7 = 3.816653826 k = 3.816653826 Simplifying k = 3.816653826

Subproblem 2

k + 7 = -10.816653826 Simplifying k + 7 = -10.816653826 Reorder the terms: 7 + k = -10.816653826 Solving 7 + k = -10.816653826 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 = -10.816653826 + -7 Combine like terms: 7 + -7 = 0 0 + k = -10.816653826 + -7 k = -10.816653826 + -7 Combine like terms: -10.816653826 + -7 = -17.816653826 k = -17.816653826 Simplifying k = -17.816653826

Solution

The solution to the problem is based on the solutions from the subproblems. k = {3.816653826, -17.816653826}

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