17x^2-33x-23=0

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Solution for 17x^2-33x-23=0 equation:


Simplifying
17x2 + -33x + -23 = 0

Reorder the terms:
-23 + -33x + 17x2 = 0

Solving
-23 + -33x + 17x2 = 0

Solving for variable 'x'.

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

Divide each side by '17'.
-1.352941176 + -1.941176471x + x2 = 0

Move the constant term to the right:

Add '1.352941176' to each side of the equation.
-1.352941176 + -1.941176471x + 1.352941176 + x2 = 0 + 1.352941176

Reorder the terms:
-1.352941176 + 1.352941176 + -1.941176471x + x2 = 0 + 1.352941176

Combine like terms: -1.352941176 + 1.352941176 = 0.000000000
0.000000000 + -1.941176471x + x2 = 0 + 1.352941176
-1.941176471x + x2 = 0 + 1.352941176

Combine like terms: 0 + 1.352941176 = 1.352941176
-1.941176471x + x2 = 1.352941176

The x term is -1.941176471x.  Take half its coefficient (-0.9705882355).
Square it (0.9420415229) and add it to both sides.

Add '0.9420415229' to each side of the equation.
-1.941176471x + 0.9420415229 + x2 = 1.352941176 + 0.9420415229

Reorder the terms:
0.9420415229 + -1.941176471x + x2 = 1.352941176 + 0.9420415229

Combine like terms: 1.352941176 + 0.9420415229 = 2.2949826989
0.9420415229 + -1.941176471x + x2 = 2.2949826989

Factor a perfect square on the left side:
(x + -0.9705882355)(x + -0.9705882355) = 2.2949826989

Calculate the square root of the right side: 1.514920031

Break this problem into two subproblems by setting 
(x + -0.9705882355) equal to 1.514920031 and -1.514920031.

Subproblem 1

x + -0.9705882355 = 1.514920031 Simplifying x + -0.9705882355 = 1.514920031 Reorder the terms: -0.9705882355 + x = 1.514920031 Solving -0.9705882355 + x = 1.514920031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9705882355' to each side of the equation. -0.9705882355 + 0.9705882355 + x = 1.514920031 + 0.9705882355 Combine like terms: -0.9705882355 + 0.9705882355 = 0.0000000000 0.0000000000 + x = 1.514920031 + 0.9705882355 x = 1.514920031 + 0.9705882355 Combine like terms: 1.514920031 + 0.9705882355 = 2.4855082665 x = 2.4855082665 Simplifying x = 2.4855082665

Subproblem 2

x + -0.9705882355 = -1.514920031 Simplifying x + -0.9705882355 = -1.514920031 Reorder the terms: -0.9705882355 + x = -1.514920031 Solving -0.9705882355 + x = -1.514920031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9705882355' to each side of the equation. -0.9705882355 + 0.9705882355 + x = -1.514920031 + 0.9705882355 Combine like terms: -0.9705882355 + 0.9705882355 = 0.0000000000 0.0000000000 + x = -1.514920031 + 0.9705882355 x = -1.514920031 + 0.9705882355 Combine like terms: -1.514920031 + 0.9705882355 = -0.5443317955 x = -0.5443317955 Simplifying x = -0.5443317955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.4855082665, -0.5443317955}

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