6x^2-2x-203x+5=

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Solution for 6x^2-2x-203x+5= equation:


Simplifying
6x2 + -2x + -203x + 5 = 0

Reorder the terms:
5 + -2x + -203x + 6x2 = 0

Combine like terms: -2x + -203x = -205x
5 + -205x + 6x2 = 0

Solving
5 + -205x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
0.8333333333 + -34.16666667x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -34.16666667x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -34.16666667x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -34.16666667x + x2 = 0 + -0.8333333333
-34.16666667x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-34.16666667x + x2 = -0.8333333333

The x term is -34.16666667x.  Take half its coefficient (-17.08333334).
Square it (291.8402780) and add it to both sides.

Add '291.8402780' to each side of the equation.
-34.16666667x + 291.8402780 + x2 = -0.8333333333 + 291.8402780

Reorder the terms:
291.8402780 + -34.16666667x + x2 = -0.8333333333 + 291.8402780

Combine like terms: -0.8333333333 + 291.8402780 = 291.0069446667
291.8402780 + -34.16666667x + x2 = 291.0069446667

Factor a perfect square on the left side:
(x + -17.08333334)(x + -17.08333334) = 291.0069446667

Calculate the square root of the right side: 17.05892566

Break this problem into two subproblems by setting 
(x + -17.08333334) equal to 17.05892566 and -17.05892566.

Subproblem 1

x + -17.08333334 = 17.05892566 Simplifying x + -17.08333334 = 17.05892566 Reorder the terms: -17.08333334 + x = 17.05892566 Solving -17.08333334 + x = 17.05892566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.08333334' to each side of the equation. -17.08333334 + 17.08333334 + x = 17.05892566 + 17.08333334 Combine like terms: -17.08333334 + 17.08333334 = 0.00000000 0.00000000 + x = 17.05892566 + 17.08333334 x = 17.05892566 + 17.08333334 Combine like terms: 17.05892566 + 17.08333334 = 34.142259 x = 34.142259 Simplifying x = 34.142259

Subproblem 2

x + -17.08333334 = -17.05892566 Simplifying x + -17.08333334 = -17.05892566 Reorder the terms: -17.08333334 + x = -17.05892566 Solving -17.08333334 + x = -17.05892566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.08333334' to each side of the equation. -17.08333334 + 17.08333334 + x = -17.05892566 + 17.08333334 Combine like terms: -17.08333334 + 17.08333334 = 0.00000000 0.00000000 + x = -17.05892566 + 17.08333334 x = -17.05892566 + 17.08333334 Combine like terms: -17.05892566 + 17.08333334 = 0.02440768 x = 0.02440768 Simplifying x = 0.02440768

Solution

The solution to the problem is based on the solutions from the subproblems. x = {34.142259, 0.02440768}

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