6x^2+134x-189=0

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Solution for 6x^2+134x-189=0 equation:


Simplifying
6x2 + 134x + -189 = 0

Reorder the terms:
-189 + 134x + 6x2 = 0

Solving
-189 + 134x + 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'.
-31.5 + 22.33333333x + x2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + 22.33333333x + 31.5 + x2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + 22.33333333x + x2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + 22.33333333x + x2 = 0 + 31.5
22.33333333x + x2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
22.33333333x + x2 = 31.5

The x term is 22.33333333x.  Take half its coefficient (11.16666667).
Square it (124.6944445) and add it to both sides.

Add '124.6944445' to each side of the equation.
22.33333333x + 124.6944445 + x2 = 31.5 + 124.6944445

Reorder the terms:
124.6944445 + 22.33333333x + x2 = 31.5 + 124.6944445

Combine like terms: 31.5 + 124.6944445 = 156.1944445
124.6944445 + 22.33333333x + x2 = 156.1944445

Factor a perfect square on the left side:
(x + 11.16666667)(x + 11.16666667) = 156.1944445

Calculate the square root of the right side: 12.497777582

Break this problem into two subproblems by setting 
(x + 11.16666667) equal to 12.497777582 and -12.497777582.

Subproblem 1

x + 11.16666667 = 12.497777582 Simplifying x + 11.16666667 = 12.497777582 Reorder the terms: 11.16666667 + x = 12.497777582 Solving 11.16666667 + x = 12.497777582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.16666667' to each side of the equation. 11.16666667 + -11.16666667 + x = 12.497777582 + -11.16666667 Combine like terms: 11.16666667 + -11.16666667 = 0.00000000 0.00000000 + x = 12.497777582 + -11.16666667 x = 12.497777582 + -11.16666667 Combine like terms: 12.497777582 + -11.16666667 = 1.331110912 x = 1.331110912 Simplifying x = 1.331110912

Subproblem 2

x + 11.16666667 = -12.497777582 Simplifying x + 11.16666667 = -12.497777582 Reorder the terms: 11.16666667 + x = -12.497777582 Solving 11.16666667 + x = -12.497777582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.16666667' to each side of the equation. 11.16666667 + -11.16666667 + x = -12.497777582 + -11.16666667 Combine like terms: 11.16666667 + -11.16666667 = 0.00000000 0.00000000 + x = -12.497777582 + -11.16666667 x = -12.497777582 + -11.16666667 Combine like terms: -12.497777582 + -11.16666667 = -23.664444252 x = -23.664444252 Simplifying x = -23.664444252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.331110912, -23.664444252}

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