9x^2-49x+60=0

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Solution for 9x^2-49x+60=0 equation: 


Simplifying
9x2 + -49x + 60 = 0

Reorder the terms:
60 + -49x + 9x2 = 0

Solving
60 + -49x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
6.666666667 + -5.444444444x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -5.444444444x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -5.444444444x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -5.444444444x + x2 = 0 + -6.666666667
-5.444444444x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-5.444444444x + x2 = -6.666666667

The x term is -5.444444444x.  Take half its coefficient (-2.722222222).
Square it (7.410493826) and add it to both sides.

Add '7.410493826' to each side of the equation.
-5.444444444x + 7.410493826 + x2 = -6.666666667 + 7.410493826

Reorder the terms:
7.410493826 + -5.444444444x + x2 = -6.666666667 + 7.410493826

Combine like terms: -6.666666667 + 7.410493826 = 0.743827159
7.410493826 + -5.444444444x + x2 = 0.743827159

Factor a perfect square on the left side:
(x + -2.722222222)(x + -2.722222222) = 0.743827159

Calculate the square root of the right side: 0.862454149

Break this problem into two subproblems by setting 
(x + -2.722222222) equal to 0.862454149 and -0.862454149.


Subproblem 1
x + -2.722222222 = 0.862454149

Simplifying
x + -2.722222222 = 0.862454149

Reorder the terms:
-2.722222222 + x = 0.862454149

Solving
-2.722222222 + x = 0.862454149

Solving for variable 'x'.

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

Add '2.722222222' to each side of the equation.
-2.722222222 + 2.722222222 + x = 0.862454149 + 2.722222222

Combine like terms: -2.722222222 + 2.722222222 = 0.000000000
0.000000000 + x = 0.862454149 + 2.722222222
x = 0.862454149 + 2.722222222

Combine like terms: 0.862454149 + 2.722222222 = 3.584676371
x = 3.584676371

Simplifying
x = 3.584676371


Subproblem 2
x + -2.722222222 = -0.862454149

Simplifying
x + -2.722222222 = -0.862454149

Reorder the terms:
-2.722222222 + x = -0.862454149

Solving
-2.722222222 + x = -0.862454149

Solving for variable 'x'.

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

Add '2.722222222' to each side of the equation.
-2.722222222 + 2.722222222 + x = -0.862454149 + 2.722222222

Combine like terms: -2.722222222 + 2.722222222 = 0.000000000
0.000000000 + x = -0.862454149 + 2.722222222
x = -0.862454149 + 2.722222222

Combine like terms: -0.862454149 + 2.722222222 = 1.859768073
x = 1.859768073

Simplifying
x = 1.859768073


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.584676371, 1.859768073}

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