60x^2-44x-35=0

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Solution for 60x^2-44x-35=0 equation: 


Simplifying
60x2 + -44x + -35 = 0

Reorder the terms:
-35 + -44x + 60x2 = 0

Solving
-35 + -44x + 60x2 = 0

Solving for variable 'x'.

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

Divide each side by '60'.
-0.5833333333 + -0.7333333333x + x2 = 0

Move the constant term to the right:

Add '0.5833333333' to each side of the equation.
-0.5833333333 + -0.7333333333x + 0.5833333333 + x2 = 0 + 0.5833333333

Reorder the terms:
-0.5833333333 + 0.5833333333 + -0.7333333333x + x2 = 0 + 0.5833333333

Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000
0.0000000000 + -0.7333333333x + x2 = 0 + 0.5833333333
-0.7333333333x + x2 = 0 + 0.5833333333

Combine like terms: 0 + 0.5833333333 = 0.5833333333
-0.7333333333x + x2 = 0.5833333333

The x term is -0.7333333333x.  Take half its coefficient (-0.3666666667).
Square it (0.1344444445) and add it to both sides.

Add '0.1344444445' to each side of the equation.
-0.7333333333x + 0.1344444445 + x2 = 0.5833333333 + 0.1344444445

Reorder the terms:
0.1344444445 + -0.7333333333x + x2 = 0.5833333333 + 0.1344444445

Combine like terms: 0.5833333333 + 0.1344444445 = 0.7177777778
0.1344444445 + -0.7333333333x + x2 = 0.7177777778

Factor a perfect square on the left side:
(x + -0.3666666667)(x + -0.3666666667) = 0.7177777778

Calculate the square root of the right side: 0.847217668

Break this problem into two subproblems by setting 
(x + -0.3666666667) equal to 0.847217668 and -0.847217668.


Subproblem 1
x + -0.3666666667 = 0.847217668

Simplifying
x + -0.3666666667 = 0.847217668

Reorder the terms:
-0.3666666667 + x = 0.847217668

Solving
-0.3666666667 + x = 0.847217668

Solving for variable 'x'.

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

Add '0.3666666667' to each side of the equation.
-0.3666666667 + 0.3666666667 + x = 0.847217668 + 0.3666666667

Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000
0.0000000000 + x = 0.847217668 + 0.3666666667
x = 0.847217668 + 0.3666666667

Combine like terms: 0.847217668 + 0.3666666667 = 1.2138843347
x = 1.2138843347

Simplifying
x = 1.2138843347


Subproblem 2
x + -0.3666666667 = -0.847217668

Simplifying
x + -0.3666666667 = -0.847217668

Reorder the terms:
-0.3666666667 + x = -0.847217668

Solving
-0.3666666667 + x = -0.847217668

Solving for variable 'x'.

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

Add '0.3666666667' to each side of the equation.
-0.3666666667 + 0.3666666667 + x = -0.847217668 + 0.3666666667

Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000
0.0000000000 + x = -0.847217668 + 0.3666666667
x = -0.847217668 + 0.3666666667

Combine like terms: -0.847217668 + 0.3666666667 = -0.4805510013
x = -0.4805510013

Simplifying
x = -0.4805510013


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2138843347, -0.4805510013}

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