35x^2-12x=6

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Solution for 35x^2-12x=6 equation:


Simplifying
35x2 + -12x = 6

Reorder the terms:
-12x + 35x2 = 6

Solving
-12x + 35x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + -12x + 35x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -12x + 35x2 = 0

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

Divide each side by '35'.
-0.1714285714 + -0.3428571429x + x2 = 0

Move the constant term to the right:

Add '0.1714285714' to each side of the equation.
-0.1714285714 + -0.3428571429x + 0.1714285714 + x2 = 0 + 0.1714285714

Reorder the terms:
-0.1714285714 + 0.1714285714 + -0.3428571429x + x2 = 0 + 0.1714285714

Combine like terms: -0.1714285714 + 0.1714285714 = 0.0000000000
0.0000000000 + -0.3428571429x + x2 = 0 + 0.1714285714
-0.3428571429x + x2 = 0 + 0.1714285714

Combine like terms: 0 + 0.1714285714 = 0.1714285714
-0.3428571429x + x2 = 0.1714285714

The x term is -0.3428571429x.  Take half its coefficient (-0.1714285715).
Square it (0.02938775513) and add it to both sides.

Add '0.02938775513' to each side of the equation.
-0.3428571429x + 0.02938775513 + x2 = 0.1714285714 + 0.02938775513

Reorder the terms:
0.02938775513 + -0.3428571429x + x2 = 0.1714285714 + 0.02938775513

Combine like terms: 0.1714285714 + 0.02938775513 = 0.20081632653
0.02938775513 + -0.3428571429x + x2 = 0.20081632653

Factor a perfect square on the left side:
(x + -0.1714285715)(x + -0.1714285715) = 0.20081632653

Calculate the square root of the right side: 0.448125347

Break this problem into two subproblems by setting 
(x + -0.1714285715) equal to 0.448125347 and -0.448125347.

Subproblem 1

x + -0.1714285715 = 0.448125347 Simplifying x + -0.1714285715 = 0.448125347 Reorder the terms: -0.1714285715 + x = 0.448125347 Solving -0.1714285715 + x = 0.448125347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1714285715' to each side of the equation. -0.1714285715 + 0.1714285715 + x = 0.448125347 + 0.1714285715 Combine like terms: -0.1714285715 + 0.1714285715 = 0.0000000000 0.0000000000 + x = 0.448125347 + 0.1714285715 x = 0.448125347 + 0.1714285715 Combine like terms: 0.448125347 + 0.1714285715 = 0.6195539185 x = 0.6195539185 Simplifying x = 0.6195539185

Subproblem 2

x + -0.1714285715 = -0.448125347 Simplifying x + -0.1714285715 = -0.448125347 Reorder the terms: -0.1714285715 + x = -0.448125347 Solving -0.1714285715 + x = -0.448125347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1714285715' to each side of the equation. -0.1714285715 + 0.1714285715 + x = -0.448125347 + 0.1714285715 Combine like terms: -0.1714285715 + 0.1714285715 = 0.0000000000 0.0000000000 + x = -0.448125347 + 0.1714285715 x = -0.448125347 + 0.1714285715 Combine like terms: -0.448125347 + 0.1714285715 = -0.2766967755 x = -0.2766967755 Simplifying x = -0.2766967755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6195539185, -0.2766967755}

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