2x^2-14x-74=0

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


Simplifying
2x2 + -14x + -74 = 0

Reorder the terms:
-74 + -14x + 2x2 = 0

Solving
-74 + -14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-37 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-37 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-37 + -7x + x2 = 0

Solving
-37 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -7x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + -7x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -7x + x2 = 0 + 37
-7x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
-7x + x2 = 37

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 37 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 37 + 12.25

Combine like terms: 37 + 12.25 = 49.25
12.25 + -7x + x2 = 49.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(x + -3.5) equal to 7.017834424 and -7.017834424.


Subproblem 1
x + -3.5 = 7.017834424

Simplifying
x + -3.5 = 7.017834424

Reorder the terms:
-3.5 + x = 7.017834424

Solving
-3.5 + x = 7.017834424

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 7.017834424 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 7.017834424 + 3.5
x = 7.017834424 + 3.5

Combine like terms: 7.017834424 + 3.5 = 10.517834424
x = 10.517834424

Simplifying
x = 10.517834424


Subproblem 2
x + -3.5 = -7.017834424

Simplifying
x + -3.5 = -7.017834424

Reorder the terms:
-3.5 + x = -7.017834424

Solving
-3.5 + x = -7.017834424

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -7.017834424 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -7.017834424 + 3.5
x = -7.017834424 + 3.5

Combine like terms: -7.017834424 + 3.5 = -3.517834424
x = -3.517834424

Simplifying
x = -3.517834424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.517834424, -3.517834424}
Solution
x = {10.517834424, -3.517834424}

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