30x^2-14x-5=0

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Solution for 30x^2-14x-5=0 equation: 


Simplifying
30x2 + -14x + -5 = 0

Reorder the terms:
-5 + -14x + 30x2 = 0

Solving
-5 + -14x + 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'.
-0.1666666667 + -0.4666666667x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.4666666667x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.4666666667x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.4666666667x + x2 = 0 + 0.1666666667
-0.4666666667x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-0.4666666667x + x2 = 0.1666666667

The x term is -0.4666666667x.  Take half its coefficient (-0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
-0.4666666667x + 0.05444444448 + x2 = 0.1666666667 + 0.05444444448

Reorder the terms:
0.05444444448 + -0.4666666667x + x2 = 0.1666666667 + 0.05444444448

Combine like terms: 0.1666666667 + 0.05444444448 = 0.22111111118
0.05444444448 + -0.4666666667x + x2 = 0.22111111118

Factor a perfect square on the left side:
(x + -0.2333333334)(x + -0.2333333334) = 0.22111111118

Calculate the square root of the right side: 0.470224533

Break this problem into two subproblems by setting 
(x + -0.2333333334) equal to 0.470224533 and -0.470224533.


Subproblem 1
x + -0.2333333334 = 0.470224533

Simplifying
x + -0.2333333334 = 0.470224533

Reorder the terms:
-0.2333333334 + x = 0.470224533

Solving
-0.2333333334 + x = 0.470224533

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = 0.470224533 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = 0.470224533 + 0.2333333334
x = 0.470224533 + 0.2333333334

Combine like terms: 0.470224533 + 0.2333333334 = 0.7035578664
x = 0.7035578664

Simplifying
x = 0.7035578664


Subproblem 2
x + -0.2333333334 = -0.470224533

Simplifying
x + -0.2333333334 = -0.470224533

Reorder the terms:
-0.2333333334 + x = -0.470224533

Solving
-0.2333333334 + x = -0.470224533

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = -0.470224533 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = -0.470224533 + 0.2333333334
x = -0.470224533 + 0.2333333334

Combine like terms: -0.470224533 + 0.2333333334 = -0.2368911996
x = -0.2368911996

Simplifying
x = -0.2368911996


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7035578664, -0.2368911996}

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