15x^2-29x-4=0

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Solution for 15x^2-29x-4=0 equation: 


Simplifying
15x2 + -29x + -4 = 0

Reorder the terms:
-4 + -29x + 15x2 = 0

Solving
-4 + -29x + 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'.
-0.2666666667 + -1.933333333x + x2 = 0

Move the constant term to the right:

Add '0.2666666667' to each side of the equation.
-0.2666666667 + -1.933333333x + 0.2666666667 + x2 = 0 + 0.2666666667

Reorder the terms:
-0.2666666667 + 0.2666666667 + -1.933333333x + x2 = 0 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + -1.933333333x + x2 = 0 + 0.2666666667
-1.933333333x + x2 = 0 + 0.2666666667

Combine like terms: 0 + 0.2666666667 = 0.2666666667
-1.933333333x + x2 = 0.2666666667

The x term is -1.933333333x.  Take half its coefficient (-0.9666666665).
Square it (0.9344444441) and add it to both sides.

Add '0.9344444441' to each side of the equation.
-1.933333333x + 0.9344444441 + x2 = 0.2666666667 + 0.9344444441

Reorder the terms:
0.9344444441 + -1.933333333x + x2 = 0.2666666667 + 0.9344444441

Combine like terms: 0.2666666667 + 0.9344444441 = 1.2011111108
0.9344444441 + -1.933333333x + x2 = 1.2011111108

Factor a perfect square on the left side:
(x + -0.9666666665)(x + -0.9666666665) = 1.2011111108

Calculate the square root of the right side: 1.095952148

Break this problem into two subproblems by setting 
(x + -0.9666666665) equal to 1.095952148 and -1.095952148.


Subproblem 1
x + -0.9666666665 = 1.095952148

Simplifying
x + -0.9666666665 = 1.095952148

Reorder the terms:
-0.9666666665 + x = 1.095952148

Solving
-0.9666666665 + x = 1.095952148

Solving for variable 'x'.

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

Add '0.9666666665' to each side of the equation.
-0.9666666665 + 0.9666666665 + x = 1.095952148 + 0.9666666665

Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000
0.0000000000 + x = 1.095952148 + 0.9666666665
x = 1.095952148 + 0.9666666665

Combine like terms: 1.095952148 + 0.9666666665 = 2.0626188145
x = 2.0626188145

Simplifying
x = 2.0626188145


Subproblem 2
x + -0.9666666665 = -1.095952148

Simplifying
x + -0.9666666665 = -1.095952148

Reorder the terms:
-0.9666666665 + x = -1.095952148

Solving
-0.9666666665 + x = -1.095952148

Solving for variable 'x'.

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

Add '0.9666666665' to each side of the equation.
-0.9666666665 + 0.9666666665 + x = -1.095952148 + 0.9666666665

Combine like terms: -0.9666666665 + 0.9666666665 = 0.0000000000
0.0000000000 + x = -1.095952148 + 0.9666666665
x = -1.095952148 + 0.9666666665

Combine like terms: -1.095952148 + 0.9666666665 = -0.1292854815
x = -0.1292854815

Simplifying
x = -0.1292854815


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0626188145, -0.1292854815}

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