x*x+1.37x+1=0.63

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Solution for x*x+1.37x+1=0.63 equation: 


Simplifying
x * x + 1.37x + 1 = 0.63

Multiply x * x
x2 + 1.37x + 1 = 0.63

Reorder the terms:
1 + 1.37x + x2 = 0.63

Solving
1 + 1.37x + x2 = 0.63

Solving for variable 'x'.

Reorder the terms:
1 + -0.63 + 1.37x + x2 = 0.63 + -0.63

Combine like terms: 1 + -0.63 = 0.37
0.37 + 1.37x + x2 = 0.63 + -0.63

Combine like terms: 0.63 + -0.63 = 0.00
0.37 + 1.37x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-0.37' to each side of the equation.
0.37 + 1.37x + -0.37 + x2 = 0.00 + -0.37

Reorder the terms:
0.37 + -0.37 + 1.37x + x2 = 0.00 + -0.37

Combine like terms: 0.37 + -0.37 = 0.00
0.00 + 1.37x + x2 = 0.00 + -0.37
1.37x + x2 = 0.00 + -0.37

Combine like terms: 0.00 + -0.37 = -0.37
1.37x + x2 = -0.37

The x term is 1.37x.  Take half its coefficient (0.685).
Square it (0.469225) and add it to both sides.

Add '0.469225' to each side of the equation.
1.37x + 0.469225 + x2 = -0.37 + 0.469225

Reorder the terms:
0.469225 + 1.37x + x2 = -0.37 + 0.469225

Combine like terms: -0.37 + 0.469225 = 0.099225
0.469225 + 1.37x + x2 = 0.099225

Factor a perfect square on the left side:
(x + 0.685)(x + 0.685) = 0.099225

Calculate the square root of the right side: 0.315

Break this problem into two subproblems by setting 
(x + 0.685) equal to 0.315 and -0.315.


Subproblem 1
x + 0.685 = 0.315

Simplifying
x + 0.685 = 0.315

Reorder the terms:
0.685 + x = 0.315

Solving
0.685 + x = 0.315

Solving for variable 'x'.

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

Add '-0.685' to each side of the equation.
0.685 + -0.685 + x = 0.315 + -0.685

Combine like terms: 0.685 + -0.685 = 0.000
0.000 + x = 0.315 + -0.685
x = 0.315 + -0.685

Combine like terms: 0.315 + -0.685 = -0.37
x = -0.37

Simplifying
x = -0.37


Subproblem 2
x + 0.685 = -0.315

Simplifying
x + 0.685 = -0.315

Reorder the terms:
0.685 + x = -0.315

Solving
0.685 + x = -0.315

Solving for variable 'x'.

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

Add '-0.685' to each side of the equation.
0.685 + -0.685 + x = -0.315 + -0.685

Combine like terms: 0.685 + -0.685 = 0.000
0.000 + x = -0.315 + -0.685
x = -0.315 + -0.685

Combine like terms: -0.315 + -0.685 = -1
x = -1

Simplifying
x = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.37, -1}

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