187x^2-172x-33=0

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Solution for 187x^2-172x-33=0 equation:


Simplifying
187x2 + -172x + -33 = 0

Reorder the terms:
-33 + -172x + 187x2 = 0

Solving
-33 + -172x + 187x2 = 0

Solving for variable 'x'.

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

Divide each side by '187'.
-0.1764705882 + -0.9197860963x + x2 = 0

Move the constant term to the right:

Add '0.1764705882' to each side of the equation.
-0.1764705882 + -0.9197860963x + 0.1764705882 + x2 = 0 + 0.1764705882

Reorder the terms:
-0.1764705882 + 0.1764705882 + -0.9197860963x + x2 = 0 + 0.1764705882

Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000
0.0000000000 + -0.9197860963x + x2 = 0 + 0.1764705882
-0.9197860963x + x2 = 0 + 0.1764705882

Combine like terms: 0 + 0.1764705882 = 0.1764705882
-0.9197860963x + x2 = 0.1764705882

The x term is -0.9197860963x.  Take half its coefficient (-0.4598930482).
Square it (0.2115016158) and add it to both sides.

Add '0.2115016158' to each side of the equation.
-0.9197860963x + 0.2115016158 + x2 = 0.1764705882 + 0.2115016158

Reorder the terms:
0.2115016158 + -0.9197860963x + x2 = 0.1764705882 + 0.2115016158

Combine like terms: 0.1764705882 + 0.2115016158 = 0.387972204
0.2115016158 + -0.9197860963x + x2 = 0.387972204

Factor a perfect square on the left side:
(x + -0.4598930482)(x + -0.4598930482) = 0.387972204

Calculate the square root of the right side: 0.622874148

Break this problem into two subproblems by setting 
(x + -0.4598930482) equal to 0.622874148 and -0.622874148.

Subproblem 1

x + -0.4598930482 = 0.622874148 Simplifying x + -0.4598930482 = 0.622874148 Reorder the terms: -0.4598930482 + x = 0.622874148 Solving -0.4598930482 + x = 0.622874148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4598930482' to each side of the equation. -0.4598930482 + 0.4598930482 + x = 0.622874148 + 0.4598930482 Combine like terms: -0.4598930482 + 0.4598930482 = 0.0000000000 0.0000000000 + x = 0.622874148 + 0.4598930482 x = 0.622874148 + 0.4598930482 Combine like terms: 0.622874148 + 0.4598930482 = 1.0827671962 x = 1.0827671962 Simplifying x = 1.0827671962

Subproblem 2

x + -0.4598930482 = -0.622874148 Simplifying x + -0.4598930482 = -0.622874148 Reorder the terms: -0.4598930482 + x = -0.622874148 Solving -0.4598930482 + x = -0.622874148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4598930482' to each side of the equation. -0.4598930482 + 0.4598930482 + x = -0.622874148 + 0.4598930482 Combine like terms: -0.4598930482 + 0.4598930482 = 0.0000000000 0.0000000000 + x = -0.622874148 + 0.4598930482 x = -0.622874148 + 0.4598930482 Combine like terms: -0.622874148 + 0.4598930482 = -0.1629810998 x = -0.1629810998 Simplifying x = -0.1629810998

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.0827671962, -0.1629810998}

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