43-17x-15x^2=0

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Solution for 43-17x-15x^2=0 equation:


Simplifying
43 + -17x + -15x2 = 0

Solving
43 + -17x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-2.866666667 + 1.133333333x + x2 = 0

Move the constant term to the right:

Add '2.866666667' to each side of the equation.
-2.866666667 + 1.133333333x + 2.866666667 + x2 = 0 + 2.866666667

Reorder the terms:
-2.866666667 + 2.866666667 + 1.133333333x + x2 = 0 + 2.866666667

Combine like terms: -2.866666667 + 2.866666667 = 0.000000000
0.000000000 + 1.133333333x + x2 = 0 + 2.866666667
1.133333333x + x2 = 0 + 2.866666667

Combine like terms: 0 + 2.866666667 = 2.866666667
1.133333333x + x2 = 2.866666667

The x term is 1.133333333x.  Take half its coefficient (0.5666666665).
Square it (0.3211111109) and add it to both sides.

Add '0.3211111109' to each side of the equation.
1.133333333x + 0.3211111109 + x2 = 2.866666667 + 0.3211111109

Reorder the terms:
0.3211111109 + 1.133333333x + x2 = 2.866666667 + 0.3211111109

Combine like terms: 2.866666667 + 0.3211111109 = 3.1877777779
0.3211111109 + 1.133333333x + x2 = 3.1877777779

Factor a perfect square on the left side:
(x + 0.5666666665)(x + 0.5666666665) = 3.1877777779

Calculate the square root of the right side: 1.785434899

Break this problem into two subproblems by setting 
(x + 0.5666666665) equal to 1.785434899 and -1.785434899.

Subproblem 1

x + 0.5666666665 = 1.785434899 Simplifying x + 0.5666666665 = 1.785434899 Reorder the terms: 0.5666666665 + x = 1.785434899 Solving 0.5666666665 + x = 1.785434899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5666666665' to each side of the equation. 0.5666666665 + -0.5666666665 + x = 1.785434899 + -0.5666666665 Combine like terms: 0.5666666665 + -0.5666666665 = 0.0000000000 0.0000000000 + x = 1.785434899 + -0.5666666665 x = 1.785434899 + -0.5666666665 Combine like terms: 1.785434899 + -0.5666666665 = 1.2187682325 x = 1.2187682325 Simplifying x = 1.2187682325

Subproblem 2

x + 0.5666666665 = -1.785434899 Simplifying x + 0.5666666665 = -1.785434899 Reorder the terms: 0.5666666665 + x = -1.785434899 Solving 0.5666666665 + x = -1.785434899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5666666665' to each side of the equation. 0.5666666665 + -0.5666666665 + x = -1.785434899 + -0.5666666665 Combine like terms: 0.5666666665 + -0.5666666665 = 0.0000000000 0.0000000000 + x = -1.785434899 + -0.5666666665 x = -1.785434899 + -0.5666666665 Combine like terms: -1.785434899 + -0.5666666665 = -2.3521015655 x = -2.3521015655 Simplifying x = -2.3521015655

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2187682325, -2.3521015655}

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