30x^2-77x-60=0

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Solution for 30x^2-77x-60=0 equation:


Simplifying
30x2 + -77x + -60 = 0

Reorder the terms:
-60 + -77x + 30x2 = 0

Solving
-60 + -77x + 30x2 = 0

Solving for variable 'x'.

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

Divide each side by '30'.
-2 + -2.566666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2.566666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -2.566666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2.566666667x + x2 = 0 + 2
-2.566666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2.566666667x + x2 = 2

The x term is -2.566666667x.  Take half its coefficient (-1.283333334).
Square it (1.646944446) and add it to both sides.

Add '1.646944446' to each side of the equation.
-2.566666667x + 1.646944446 + x2 = 2 + 1.646944446

Reorder the terms:
1.646944446 + -2.566666667x + x2 = 2 + 1.646944446

Combine like terms: 2 + 1.646944446 = 3.646944446
1.646944446 + -2.566666667x + x2 = 3.646944446

Factor a perfect square on the left side:
(x + -1.283333334)(x + -1.283333334) = 3.646944446

Calculate the square root of the right side: 1.909697475

Break this problem into two subproblems by setting 
(x + -1.283333334) equal to 1.909697475 and -1.909697475.

Subproblem 1

x + -1.283333334 = 1.909697475 Simplifying x + -1.283333334 = 1.909697475 Reorder the terms: -1.283333334 + x = 1.909697475 Solving -1.283333334 + x = 1.909697475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.283333334' to each side of the equation. -1.283333334 + 1.283333334 + x = 1.909697475 + 1.283333334 Combine like terms: -1.283333334 + 1.283333334 = 0.000000000 0.000000000 + x = 1.909697475 + 1.283333334 x = 1.909697475 + 1.283333334 Combine like terms: 1.909697475 + 1.283333334 = 3.193030809 x = 3.193030809 Simplifying x = 3.193030809

Subproblem 2

x + -1.283333334 = -1.909697475 Simplifying x + -1.283333334 = -1.909697475 Reorder the terms: -1.283333334 + x = -1.909697475 Solving -1.283333334 + x = -1.909697475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.283333334' to each side of the equation. -1.283333334 + 1.283333334 + x = -1.909697475 + 1.283333334 Combine like terms: -1.283333334 + 1.283333334 = 0.000000000 0.000000000 + x = -1.909697475 + 1.283333334 x = -1.909697475 + 1.283333334 Combine like terms: -1.909697475 + 1.283333334 = -0.626364141 x = -0.626364141 Simplifying x = -0.626364141

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.193030809, -0.626364141}

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