9x^2+77x+60=0

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Solution for 9x^2+77x+60=0 equation:


Simplifying
9x2 + 77x + 60 = 0

Reorder the terms:
60 + 77x + 9x2 = 0

Solving
60 + 77x + 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 + 8.555555556x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + 8.555555556x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + 8.555555556x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + 8.555555556x + x2 = 0 + -6.666666667
8.555555556x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
8.555555556x + x2 = -6.666666667

The x term is 8.555555556x.  Take half its coefficient (4.277777778).
Square it (18.29938272) and add it to both sides.

Add '18.29938272' to each side of the equation.
8.555555556x + 18.29938272 + x2 = -6.666666667 + 18.29938272

Reorder the terms:
18.29938272 + 8.555555556x + x2 = -6.666666667 + 18.29938272

Combine like terms: -6.666666667 + 18.29938272 = 11.632716053
18.29938272 + 8.555555556x + x2 = 11.632716053

Factor a perfect square on the left side:
(x + 4.277777778)(x + 4.277777778) = 11.632716053

Calculate the square root of the right side: 3.410676773

Break this problem into two subproblems by setting 
(x + 4.277777778) equal to 3.410676773 and -3.410676773.

Subproblem 1

x + 4.277777778 = 3.410676773 Simplifying x + 4.277777778 = 3.410676773 Reorder the terms: 4.277777778 + x = 3.410676773 Solving 4.277777778 + x = 3.410676773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.277777778' to each side of the equation. 4.277777778 + -4.277777778 + x = 3.410676773 + -4.277777778 Combine like terms: 4.277777778 + -4.277777778 = 0.000000000 0.000000000 + x = 3.410676773 + -4.277777778 x = 3.410676773 + -4.277777778 Combine like terms: 3.410676773 + -4.277777778 = -0.867101005 x = -0.867101005 Simplifying x = -0.867101005

Subproblem 2

x + 4.277777778 = -3.410676773 Simplifying x + 4.277777778 = -3.410676773 Reorder the terms: 4.277777778 + x = -3.410676773 Solving 4.277777778 + x = -3.410676773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.277777778' to each side of the equation. 4.277777778 + -4.277777778 + x = -3.410676773 + -4.277777778 Combine like terms: 4.277777778 + -4.277777778 = 0.000000000 0.000000000 + x = -3.410676773 + -4.277777778 x = -3.410676773 + -4.277777778 Combine like terms: -3.410676773 + -4.277777778 = -7.688454551 x = -7.688454551 Simplifying x = -7.688454551

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.867101005, -7.688454551}

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