30x^2-52x-7=0

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Solution for 30x^2-52x-7=0 equation: 


Simplifying
30x2 + -52x + -7 = 0

Reorder the terms:
-7 + -52x + 30x2 = 0

Solving
-7 + -52x + 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'.
-0.2333333333 + -1.733333333x + x2 = 0

Move the constant term to the right:

Add '0.2333333333' to each side of the equation.
-0.2333333333 + -1.733333333x + 0.2333333333 + x2 = 0 + 0.2333333333

Reorder the terms:
-0.2333333333 + 0.2333333333 + -1.733333333x + x2 = 0 + 0.2333333333

Combine like terms: -0.2333333333 + 0.2333333333 = 0.0000000000
0.0000000000 + -1.733333333x + x2 = 0 + 0.2333333333
-1.733333333x + x2 = 0 + 0.2333333333

Combine like terms: 0 + 0.2333333333 = 0.2333333333
-1.733333333x + x2 = 0.2333333333

The x term is -1.733333333x.  Take half its coefficient (-0.8666666665).
Square it (0.7511111108) and add it to both sides.

Add '0.7511111108' to each side of the equation.
-1.733333333x + 0.7511111108 + x2 = 0.2333333333 + 0.7511111108

Reorder the terms:
0.7511111108 + -1.733333333x + x2 = 0.2333333333 + 0.7511111108

Combine like terms: 0.2333333333 + 0.7511111108 = 0.9844444441
0.7511111108 + -1.733333333x + x2 = 0.9844444441

Factor a perfect square on the left side:
(x + -0.8666666665)(x + -0.8666666665) = 0.9844444441

Calculate the square root of the right side: 0.992191738

Break this problem into two subproblems by setting 
(x + -0.8666666665) equal to 0.992191738 and -0.992191738.


Subproblem 1
x + -0.8666666665 = 0.992191738

Simplifying
x + -0.8666666665 = 0.992191738

Reorder the terms:
-0.8666666665 + x = 0.992191738

Solving
-0.8666666665 + x = 0.992191738

Solving for variable 'x'.

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

Add '0.8666666665' to each side of the equation.
-0.8666666665 + 0.8666666665 + x = 0.992191738 + 0.8666666665

Combine like terms: -0.8666666665 + 0.8666666665 = 0.0000000000
0.0000000000 + x = 0.992191738 + 0.8666666665
x = 0.992191738 + 0.8666666665

Combine like terms: 0.992191738 + 0.8666666665 = 1.8588584045
x = 1.8588584045

Simplifying
x = 1.8588584045


Subproblem 2
x + -0.8666666665 = -0.992191738

Simplifying
x + -0.8666666665 = -0.992191738

Reorder the terms:
-0.8666666665 + x = -0.992191738

Solving
-0.8666666665 + x = -0.992191738

Solving for variable 'x'.

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

Add '0.8666666665' to each side of the equation.
-0.8666666665 + 0.8666666665 + x = -0.992191738 + 0.8666666665

Combine like terms: -0.8666666665 + 0.8666666665 = 0.0000000000
0.0000000000 + x = -0.992191738 + 0.8666666665
x = -0.992191738 + 0.8666666665

Combine like terms: -0.992191738 + 0.8666666665 = -0.1255250715
x = -0.1255250715

Simplifying
x = -0.1255250715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8588584045, -0.1255250715}

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