-2x^2+79x-35=0

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Solution for -2x^2+79x-35=0 equation:


Simplifying
-2x2 + 79x + -35 = 0

Reorder the terms:
-35 + 79x + -2x2 = 0

Solving
-35 + 79x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
17.5 + -39.5x + x2 = 0

Move the constant term to the right:

Add '-17.5' to each side of the equation.
17.5 + -39.5x + -17.5 + x2 = 0 + -17.5

Reorder the terms:
17.5 + -17.5 + -39.5x + x2 = 0 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + -39.5x + x2 = 0 + -17.5
-39.5x + x2 = 0 + -17.5

Combine like terms: 0 + -17.5 = -17.5
-39.5x + x2 = -17.5

The x term is -39.5x.  Take half its coefficient (-19.75).
Square it (390.0625) and add it to both sides.

Add '390.0625' to each side of the equation.
-39.5x + 390.0625 + x2 = -17.5 + 390.0625

Reorder the terms:
390.0625 + -39.5x + x2 = -17.5 + 390.0625

Combine like terms: -17.5 + 390.0625 = 372.5625
390.0625 + -39.5x + x2 = 372.5625

Factor a perfect square on the left side:
(x + -19.75)(x + -19.75) = 372.5625

Calculate the square root of the right side: 19.301878147

Break this problem into two subproblems by setting 
(x + -19.75) equal to 19.301878147 and -19.301878147.


Subproblem 1
x + -19.75 = 19.301878147

Simplifying
x + -19.75 = 19.301878147

Reorder the terms:
-19.75 + x = 19.301878147

Solving
-19.75 + x = 19.301878147

Solving for variable 'x'.

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

Add '19.75' to each side of the equation.
-19.75 + 19.75 + x = 19.301878147 + 19.75

Combine like terms: -19.75 + 19.75 = 0.00
0.00 + x = 19.301878147 + 19.75
x = 19.301878147 + 19.75

Combine like terms: 19.301878147 + 19.75 = 39.051878147
x = 39.051878147

Simplifying
x = 39.051878147


Subproblem 2
x + -19.75 = -19.301878147

Simplifying
x + -19.75 = -19.301878147

Reorder the terms:
-19.75 + x = -19.301878147

Solving
-19.75 + x = -19.301878147

Solving for variable 'x'.

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

Add '19.75' to each side of the equation.
-19.75 + 19.75 + x = -19.301878147 + 19.75

Combine like terms: -19.75 + 19.75 = 0.00
0.00 + x = -19.301878147 + 19.75
x = -19.301878147 + 19.75

Combine like terms: -19.301878147 + 19.75 = 0.448121853
x = 0.448121853

Simplifying
x = 0.448121853


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {39.051878147, 0.448121853}

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