=18x^2+6x-5

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Solution for =18x^2+6x-5 equation:


Simplifying
0 = 18x2 + 6x + -5

Reorder the terms:
0 = -5 + 6x + 18x2

Solving
0 = -5 + 6x + 18x2

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + -6x + -18x2 = -5 + 6x + 18x2 + 5 + -6x + -18x2

Reorder the terms:
5 + -6x + -18x2 = -5 + 5 + 6x + -6x + 18x2 + -18x2

Combine like terms: -5 + 5 = 0
5 + -6x + -18x2 = 0 + 6x + -6x + 18x2 + -18x2
5 + -6x + -18x2 = 6x + -6x + 18x2 + -18x2

Combine like terms: 6x + -6x = 0
5 + -6x + -18x2 = 0 + 18x2 + -18x2
5 + -6x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
5 + -6x + -18x2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-0.2777777778 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.3333333333x + 0.2777777778 + x2 = 0 + 0.2777777778

Reorder the terms:
-0.2777777778 + 0.2777777778 + 0.3333333333x + x2 = 0 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + 0.3333333333x + x2 = 0 + 0.2777777778
0.3333333333x + x2 = 0 + 0.2777777778

Combine like terms: 0 + 0.2777777778 = 0.2777777778
0.3333333333x + x2 = 0.2777777778

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 0.2777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 0.2777777778 + 0.02777777779

Combine like terms: 0.2777777778 + 0.02777777779 = 0.30555555559
0.02777777779 + 0.3333333333x + x2 = 0.30555555559

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 0.30555555559

Calculate the square root of the right side: 0.552770798

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 0.552770798 and -0.552770798.

Subproblem 1

x + 0.1666666667 = 0.552770798 Simplifying x + 0.1666666667 = 0.552770798 Reorder the terms: 0.1666666667 + x = 0.552770798 Solving 0.1666666667 + x = 0.552770798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.552770798 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.552770798 + -0.1666666667 x = 0.552770798 + -0.1666666667 Combine like terms: 0.552770798 + -0.1666666667 = 0.3861041313 x = 0.3861041313 Simplifying x = 0.3861041313

Subproblem 2

x + 0.1666666667 = -0.552770798 Simplifying x + 0.1666666667 = -0.552770798 Reorder the terms: 0.1666666667 + x = -0.552770798 Solving 0.1666666667 + x = -0.552770798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.552770798 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.552770798 + -0.1666666667 x = -0.552770798 + -0.1666666667 Combine like terms: -0.552770798 + -0.1666666667 = -0.7194374647 x = -0.7194374647 Simplifying x = -0.7194374647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3861041313, -0.7194374647}

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