15x^2-77x-10=0

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Solution for 15x^2-77x-10=0 equation: 


Simplifying
15x2 + -77x + -10 = 0

Reorder the terms:
-10 + -77x + 15x2 = 0

Solving
-10 + -77x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-0.6666666667 + -5.133333333x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -5.133333333x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -5.133333333x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -5.133333333x + x2 = 0 + 0.6666666667
-5.133333333x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-5.133333333x + x2 = 0.6666666667

The x term is -5.133333333x.  Take half its coefficient (-2.566666667).
Square it (6.587777779) and add it to both sides.

Add '6.587777779' to each side of the equation.
-5.133333333x + 6.587777779 + x2 = 0.6666666667 + 6.587777779

Reorder the terms:
6.587777779 + -5.133333333x + x2 = 0.6666666667 + 6.587777779

Combine like terms: 0.6666666667 + 6.587777779 = 7.2544444457
6.587777779 + -5.133333333x + x2 = 7.2544444457

Factor a perfect square on the left side:
(x + -2.566666667)(x + -2.566666667) = 7.2544444457

Calculate the square root of the right side: 2.69340759

Break this problem into two subproblems by setting 
(x + -2.566666667) equal to 2.69340759 and -2.69340759.


Subproblem 1
x + -2.566666667 = 2.69340759

Simplifying
x + -2.566666667 = 2.69340759

Reorder the terms:
-2.566666667 + x = 2.69340759

Solving
-2.566666667 + x = 2.69340759

Solving for variable 'x'.

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

Add '2.566666667' to each side of the equation.
-2.566666667 + 2.566666667 + x = 2.69340759 + 2.566666667

Combine like terms: -2.566666667 + 2.566666667 = 0.000000000
0.000000000 + x = 2.69340759 + 2.566666667
x = 2.69340759 + 2.566666667

Combine like terms: 2.69340759 + 2.566666667 = 5.260074257
x = 5.260074257

Simplifying
x = 5.260074257


Subproblem 2
x + -2.566666667 = -2.69340759

Simplifying
x + -2.566666667 = -2.69340759

Reorder the terms:
-2.566666667 + x = -2.69340759

Solving
-2.566666667 + x = -2.69340759

Solving for variable 'x'.

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

Add '2.566666667' to each side of the equation.
-2.566666667 + 2.566666667 + x = -2.69340759 + 2.566666667

Combine like terms: -2.566666667 + 2.566666667 = 0.000000000
0.000000000 + x = -2.69340759 + 2.566666667
x = -2.69340759 + 2.566666667

Combine like terms: -2.69340759 + 2.566666667 = -0.126740923
x = -0.126740923

Simplifying
x = -0.126740923


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.260074257, -0.126740923}

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