x^2+14x-74=0

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Solution for x^2+14x-74=0 equation: 


Simplifying
x2 + 14x + -74 = 0

Reorder the terms:
-74 + 14x + x2 = 0

Solving
-74 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + 14x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + 14x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + 14x + x2 = 0 + 74
14x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
14x + x2 = 74

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

Add '49' to each side of the equation.
14x + 49 + x2 = 74 + 49

Reorder the terms:
49 + 14x + x2 = 74 + 49

Combine like terms: 74 + 49 = 123
49 + 14x + x2 = 123

Factor a perfect square on the left side:
(x + 7)(x + 7) = 123

Calculate the square root of the right side: 11.090536506

Break this problem into two subproblems by setting 
(x + 7) equal to 11.090536506 and -11.090536506.


Subproblem 1
x + 7 = 11.090536506

Simplifying
x + 7 = 11.090536506

Reorder the terms:
7 + x = 11.090536506

Solving
7 + x = 11.090536506

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 11.090536506 + -7

Combine like terms: 7 + -7 = 0
0 + x = 11.090536506 + -7
x = 11.090536506 + -7

Combine like terms: 11.090536506 + -7 = 4.090536506
x = 4.090536506

Simplifying
x = 4.090536506


Subproblem 2
x + 7 = -11.090536506

Simplifying
x + 7 = -11.090536506

Reorder the terms:
7 + x = -11.090536506

Solving
7 + x = -11.090536506

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = -11.090536506 + -7

Combine like terms: 7 + -7 = 0
0 + x = -11.090536506 + -7
x = -11.090536506 + -7

Combine like terms: -11.090536506 + -7 = -18.090536506
x = -18.090536506

Simplifying
x = -18.090536506


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.090536506, -18.090536506}

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