1.4x^2+49x+35=0

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Solution for 1.4x^2+49x+35=0 equation: 


Simplifying
1.4x2 + 49x + 35 = 0

Reorder the terms:
35 + 49x + 1.4x2 = 0

Solving
35 + 49x + 1.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.4'.
25 + 35x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 35x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 35x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 35x + x2 = 0 + -25
35x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
35x + x2 = -25

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = -25 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -25 + 306.25

Combine like terms: -25 + 306.25 = 281.25
306.25 + 35x + x2 = 281.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 281.25

Calculate the square root of the right side: 16.770509831

Break this problem into two subproblems by setting 
(x + 17.5) equal to 16.770509831 and -16.770509831.


Subproblem 1
x + 17.5 = 16.770509831

Simplifying
x + 17.5 = 16.770509831

Reorder the terms:
17.5 + x = 16.770509831

Solving
17.5 + x = 16.770509831

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 16.770509831 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 16.770509831 + -17.5
x = 16.770509831 + -17.5

Combine like terms: 16.770509831 + -17.5 = -0.729490169
x = -0.729490169

Simplifying
x = -0.729490169


Subproblem 2
x + 17.5 = -16.770509831

Simplifying
x + 17.5 = -16.770509831

Reorder the terms:
17.5 + x = -16.770509831

Solving
17.5 + x = -16.770509831

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -16.770509831 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -16.770509831 + -17.5
x = -16.770509831 + -17.5

Combine like terms: -16.770509831 + -17.5 = -34.270509831
x = -34.270509831

Simplifying
x = -34.270509831


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.729490169, -34.270509831}

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