2x^2-14x-62=0

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Solution for 2x^2-14x-62=0 equation: 


Simplifying
2x2 + -14x + -62 = 0

Reorder the terms:
-62 + -14x + 2x2 = 0

Solving
-62 + -14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + -7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-31 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-31 + -7x + x2 = 0

Solving
-31 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -7x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -7x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -7x + x2 = 0 + 31
-7x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-7x + x2 = 31

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 = 31 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 31 + 12.25

Combine like terms: 31 + 12.25 = 43.25
12.25 + -7x + x2 = 43.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.576473219 and -6.576473219.


Subproblem 1
x + -3.5 = 6.576473219

Simplifying
x + -3.5 = 6.576473219

Reorder the terms:
-3.5 + x = 6.576473219

Solving
-3.5 + x = 6.576473219

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 = 6.576473219 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 6.576473219 + 3.5
x = 6.576473219 + 3.5

Combine like terms: 6.576473219 + 3.5 = 10.076473219
x = 10.076473219

Simplifying
x = 10.076473219


Subproblem 2
x + -3.5 = -6.576473219

Simplifying
x + -3.5 = -6.576473219

Reorder the terms:
-3.5 + x = -6.576473219

Solving
-3.5 + x = -6.576473219

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 = -6.576473219 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -6.576473219 + 3.5
x = -6.576473219 + 3.5

Combine like terms: -6.576473219 + 3.5 = -3.076473219
x = -3.076473219

Simplifying
x = -3.076473219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.076473219, -3.076473219}
Solution
x = {10.076473219, -3.076473219}

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