30x^2-5x-3=0

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Solution for 30x^2-5x-3=0 equation: 


Simplifying
30x2 + -5x + -3 = 0

Reorder the terms:
-3 + -5x + 30x2 = 0

Solving
-3 + -5x + 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'.
-0.1 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.1666666667x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.1666666667x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.1666666667x + x2 = 0 + 0.1
-0.1666666667x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-0.1666666667x + x2 = 0.1

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 0.1 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 0.1 + 0.006944444447

Combine like terms: 0.1 + 0.006944444447 = 0.106944444447
0.006944444447 + -0.1666666667x + x2 = 0.106944444447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 0.106944444447

Calculate the square root of the right side: 0.327023615

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 0.327023615 and -0.327023615.


Subproblem 1
x + -0.08333333335 = 0.327023615

Simplifying
x + -0.08333333335 = 0.327023615

Reorder the terms:
-0.08333333335 + x = 0.327023615

Solving
-0.08333333335 + x = 0.327023615

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 0.327023615 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 0.327023615 + 0.08333333335
x = 0.327023615 + 0.08333333335

Combine like terms: 0.327023615 + 0.08333333335 = 0.41035694835
x = 0.41035694835

Simplifying
x = 0.41035694835


Subproblem 2
x + -0.08333333335 = -0.327023615

Simplifying
x + -0.08333333335 = -0.327023615

Reorder the terms:
-0.08333333335 + x = -0.327023615

Solving
-0.08333333335 + x = -0.327023615

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -0.327023615 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -0.327023615 + 0.08333333335
x = -0.327023615 + 0.08333333335

Combine like terms: -0.327023615 + 0.08333333335 = -0.24369028165
x = -0.24369028165

Simplifying
x = -0.24369028165


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.41035694835, -0.24369028165}

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