0.7x^2+3.7x+1=0

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Solution for 0.7x^2+3.7x+1=0 equation: 


Simplifying
0.7x2 + 3.7x + 1 = 0

Reorder the terms:
1 + 3.7x + 0.7x2 = 0

Solving
1 + 3.7x + 0.7x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.7'.
1.428571429 + 5.285714286x + x2 = 0

Move the constant term to the right:

Add '-1.428571429' to each side of the equation.
1.428571429 + 5.285714286x + -1.428571429 + x2 = 0 + -1.428571429

Reorder the terms:
1.428571429 + -1.428571429 + 5.285714286x + x2 = 0 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + 5.285714286x + x2 = 0 + -1.428571429
5.285714286x + x2 = 0 + -1.428571429

Combine like terms: 0 + -1.428571429 = -1.428571429
5.285714286x + x2 = -1.428571429

The x term is 5.285714286x.  Take half its coefficient (2.642857143).
Square it (6.984693878) and add it to both sides.

Add '6.984693878' to each side of the equation.
5.285714286x + 6.984693878 + x2 = -1.428571429 + 6.984693878

Reorder the terms:
6.984693878 + 5.285714286x + x2 = -1.428571429 + 6.984693878

Combine like terms: -1.428571429 + 6.984693878 = 5.556122449
6.984693878 + 5.285714286x + x2 = 5.556122449

Factor a perfect square on the left side:
(x + 2.642857143)(x + 2.642857143) = 5.556122449

Calculate the square root of the right side: 2.357142857

Break this problem into two subproblems by setting 
(x + 2.642857143) equal to 2.357142857 and -2.357142857.


Subproblem 1
x + 2.642857143 = 2.357142857

Simplifying
x + 2.642857143 = 2.357142857

Reorder the terms:
2.642857143 + x = 2.357142857

Solving
2.642857143 + x = 2.357142857

Solving for variable 'x'.

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

Add '-2.642857143' to each side of the equation.
2.642857143 + -2.642857143 + x = 2.357142857 + -2.642857143

Combine like terms: 2.642857143 + -2.642857143 = 0.000000000
0.000000000 + x = 2.357142857 + -2.642857143
x = 2.357142857 + -2.642857143

Combine like terms: 2.357142857 + -2.642857143 = -0.285714286
x = -0.285714286

Simplifying
x = -0.285714286


Subproblem 2
x + 2.642857143 = -2.357142857

Simplifying
x + 2.642857143 = -2.357142857

Reorder the terms:
2.642857143 + x = -2.357142857

Solving
2.642857143 + x = -2.357142857

Solving for variable 'x'.

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

Add '-2.642857143' to each side of the equation.
2.642857143 + -2.642857143 + x = -2.357142857 + -2.642857143

Combine like terms: 2.642857143 + -2.642857143 = 0.000000000
0.000000000 + x = -2.357142857 + -2.642857143
x = -2.357142857 + -2.642857143

Combine like terms: -2.357142857 + -2.642857143 = -5
x = -5

Simplifying
x = -5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.285714286, -5}

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