80=2x^2+14x

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Solution for 80=2x^2+14x equation:


Simplifying
80 = 2x2 + 14x

Reorder the terms:
80 = 14x + 2x2

Solving
80 = 14x + 2x2

Solving for variable 'x'.

Reorder the terms:
80 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
80 + -14x + -2x2 = 0 + 2x2 + -2x2
80 + -14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
80 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -7x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(40 + -7x + -1x2)' equal to zero and attempt to solve:

Simplifying
40 + -7x + -1x2 = 0

Solving
40 + -7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-40 + 7x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 7x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 7x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 7x + x2 = 0 + 40
7x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
7x + x2 = 40

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 = 40 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 40 + 12.25

Combine like terms: 40 + 12.25 = 52.25
12.25 + 7x + x2 = 52.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7.228416147 and -7.228416147.


Subproblem 1
x + 3.5 = 7.228416147

Simplifying
x + 3.5 = 7.228416147

Reorder the terms:
3.5 + x = 7.228416147

Solving
3.5 + x = 7.228416147

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 = 7.228416147 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 7.228416147 + -3.5
x = 7.228416147 + -3.5

Combine like terms: 7.228416147 + -3.5 = 3.728416147
x = 3.728416147

Simplifying
x = 3.728416147


Subproblem 2
x + 3.5 = -7.228416147

Simplifying
x + 3.5 = -7.228416147

Reorder the terms:
3.5 + x = -7.228416147

Solving
3.5 + x = -7.228416147

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 = -7.228416147 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -7.228416147 + -3.5
x = -7.228416147 + -3.5

Combine like terms: -7.228416147 + -3.5 = -10.728416147
x = -10.728416147

Simplifying
x = -10.728416147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.728416147, -10.728416147}
Solution
x = {3.728416147, -10.728416147}

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