2x^2+19x-35=0

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Solution for 2x^2+19x-35=0 equation: 


Simplifying
2x2 + 19x + -35 = 0

Reorder the terms:
-35 + 19x + 2x2 = 0

Solving
-35 + 19x + 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 + 9.5x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + 9.5x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + 9.5x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + 9.5x + x2 = 0 + 17.5
9.5x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
9.5x + x2 = 17.5

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = 17.5 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = 17.5 + 22.5625

Combine like terms: 17.5 + 22.5625 = 40.0625
22.5625 + 9.5x + x2 = 40.0625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 40.0625

Calculate the square root of the right side: 6.329494451

Break this problem into two subproblems by setting 
(x + 4.75) equal to 6.329494451 and -6.329494451.


Subproblem 1
x + 4.75 = 6.329494451

Simplifying
x + 4.75 = 6.329494451

Reorder the terms:
4.75 + x = 6.329494451

Solving
4.75 + x = 6.329494451

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 6.329494451 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 6.329494451 + -4.75
x = 6.329494451 + -4.75

Combine like terms: 6.329494451 + -4.75 = 1.579494451
x = 1.579494451

Simplifying
x = 1.579494451


Subproblem 2
x + 4.75 = -6.329494451

Simplifying
x + 4.75 = -6.329494451

Reorder the terms:
4.75 + x = -6.329494451

Solving
4.75 + x = -6.329494451

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -6.329494451 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -6.329494451 + -4.75
x = -6.329494451 + -4.75

Combine like terms: -6.329494451 + -4.75 = -11.079494451
x = -11.079494451

Simplifying
x = -11.079494451


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.579494451, -11.079494451}

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