3.5x^2-0.05x-60=0

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Solution for 3.5x^2-0.05x-60=0 equation: 


Simplifying
3.5x2 + -0.05x + -60 = 0

Reorder the terms:
-60 + -0.05x + 3.5x2 = 0

Solving
-60 + -0.05x + 3.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.5'.
-17.14285714 + -0.01428571429x + x2 = 0

Move the constant term to the right:

Add '17.14285714' to each side of the equation.
-17.14285714 + -0.01428571429x + 17.14285714 + x2 = 0 + 17.14285714

Reorder the terms:
-17.14285714 + 17.14285714 + -0.01428571429x + x2 = 0 + 17.14285714

Combine like terms: -17.14285714 + 17.14285714 = 0.00000000
0.00000000 + -0.01428571429x + x2 = 0 + 17.14285714
-0.01428571429x + x2 = 0 + 17.14285714

Combine like terms: 0 + 17.14285714 = 17.14285714
-0.01428571429x + x2 = 17.14285714

The x term is -0.01428571429x.  Take half its coefficient (-0.007142857145).
Square it (0.00005102040819) and add it to both sides.

Add '0.00005102040819' to each side of the equation.
-0.01428571429x + 0.00005102040819 + x2 = 17.14285714 + 0.00005102040819

Reorder the terms:
0.00005102040819 + -0.01428571429x + x2 = 17.14285714 + 0.00005102040819

Combine like terms: 17.14285714 + 0.00005102040819 = 17.14290816040819
0.00005102040819 + -0.01428571429x + x2 = 17.14290816040819

Factor a perfect square on the left side:
(x + -0.007142857145)(x + -0.007142857145) = 17.14290816040819

Calculate the square root of the right side: 4.140399517

Break this problem into two subproblems by setting 
(x + -0.007142857145) equal to 4.140399517 and -4.140399517.


Subproblem 1
x + -0.007142857145 = 4.140399517

Simplifying
x + -0.007142857145 = 4.140399517

Reorder the terms:
-0.007142857145 + x = 4.140399517

Solving
-0.007142857145 + x = 4.140399517

Solving for variable 'x'.

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

Add '0.007142857145' to each side of the equation.
-0.007142857145 + 0.007142857145 + x = 4.140399517 + 0.007142857145

Combine like terms: -0.007142857145 + 0.007142857145 = 0.000000000000
0.000000000000 + x = 4.140399517 + 0.007142857145
x = 4.140399517 + 0.007142857145

Combine like terms: 4.140399517 + 0.007142857145 = 4.147542374145
x = 4.147542374145

Simplifying
x = 4.147542374145


Subproblem 2
x + -0.007142857145 = -4.140399517

Simplifying
x + -0.007142857145 = -4.140399517

Reorder the terms:
-0.007142857145 + x = -4.140399517

Solving
-0.007142857145 + x = -4.140399517

Solving for variable 'x'.

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

Add '0.007142857145' to each side of the equation.
-0.007142857145 + 0.007142857145 + x = -4.140399517 + 0.007142857145

Combine like terms: -0.007142857145 + 0.007142857145 = 0.000000000000
0.000000000000 + x = -4.140399517 + 0.007142857145
x = -4.140399517 + 0.007142857145

Combine like terms: -4.140399517 + 0.007142857145 = -4.133256659855
x = -4.133256659855

Simplifying
x = -4.133256659855


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.147542374145, -4.133256659855}

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