18x^2-14x-5=0

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Solution for 18x^2-14x-5=0 equation:


Simplifying
18x2 + -14x + -5 = 0

Reorder the terms:
-5 + -14x + 18x2 = 0

Solving
-5 + -14x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
-0.2777777778 + -0.7777777778x + x2 = 0

Move the constant term to the right:

Add '0.2777777778' to each side of the equation.
-0.2777777778 + -0.7777777778x + 0.2777777778 + x2 = 0 + 0.2777777778

Reorder the terms:
-0.2777777778 + 0.2777777778 + -0.7777777778x + x2 = 0 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + -0.7777777778x + x2 = 0 + 0.2777777778
-0.7777777778x + x2 = 0 + 0.2777777778

Combine like terms: 0 + 0.2777777778 = 0.2777777778
-0.7777777778x + x2 = 0.2777777778

The x term is -0.7777777778x.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778x + 0.1512345679 + x2 = 0.2777777778 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778x + x2 = 0.2777777778 + 0.1512345679

Combine like terms: 0.2777777778 + 0.1512345679 = 0.4290123457
0.1512345679 + -0.7777777778x + x2 = 0.4290123457

Factor a perfect square on the left side:
(x + -0.3888888889)(x + -0.3888888889) = 0.4290123457

Calculate the square root of the right side: 0.65499034

Break this problem into two subproblems by setting 
(x + -0.3888888889) equal to 0.65499034 and -0.65499034.

Subproblem 1

x + -0.3888888889 = 0.65499034 Simplifying x + -0.3888888889 = 0.65499034 Reorder the terms: -0.3888888889 + x = 0.65499034 Solving -0.3888888889 + x = 0.65499034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = 0.65499034 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 0.65499034 + 0.3888888889 x = 0.65499034 + 0.3888888889 Combine like terms: 0.65499034 + 0.3888888889 = 1.0438792289 x = 1.0438792289 Simplifying x = 1.0438792289

Subproblem 2

x + -0.3888888889 = -0.65499034 Simplifying x + -0.3888888889 = -0.65499034 Reorder the terms: -0.3888888889 + x = -0.65499034 Solving -0.3888888889 + x = -0.65499034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = -0.65499034 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -0.65499034 + 0.3888888889 x = -0.65499034 + 0.3888888889 Combine like terms: -0.65499034 + 0.3888888889 = -0.2661014511 x = -0.2661014511 Simplifying x = -0.2661014511

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.0438792289, -0.2661014511}

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