-17x^2+19x+2=0

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Solution for -17x^2+19x+2=0 equation:


Simplifying
-17x2 + 19x + 2 = 0

Reorder the terms:
2 + 19x + -17x2 = 0

Solving
2 + 19x + -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'.
-0.1176470588 + -1.117647059x + x2 = 0

Move the constant term to the right:

Add '0.1176470588' to each side of the equation.
-0.1176470588 + -1.117647059x + 0.1176470588 + x2 = 0 + 0.1176470588

Reorder the terms:
-0.1176470588 + 0.1176470588 + -1.117647059x + x2 = 0 + 0.1176470588

Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000
0.0000000000 + -1.117647059x + x2 = 0 + 0.1176470588
-1.117647059x + x2 = 0 + 0.1176470588

Combine like terms: 0 + 0.1176470588 = 0.1176470588
-1.117647059x + x2 = 0.1176470588

The x term is -1.117647059x.  Take half its coefficient (-0.5588235295).
Square it (0.3122837371) and add it to both sides.

Add '0.3122837371' to each side of the equation.
-1.117647059x + 0.3122837371 + x2 = 0.1176470588 + 0.3122837371

Reorder the terms:
0.3122837371 + -1.117647059x + x2 = 0.1176470588 + 0.3122837371

Combine like terms: 0.1176470588 + 0.3122837371 = 0.4299307959
0.3122837371 + -1.117647059x + x2 = 0.4299307959

Factor a perfect square on the left side:
(x + -0.5588235295)(x + -0.5588235295) = 0.4299307959

Calculate the square root of the right side: 0.655691083

Break this problem into two subproblems by setting 
(x + -0.5588235295) equal to 0.655691083 and -0.655691083.

Subproblem 1

x + -0.5588235295 = 0.655691083 Simplifying x + -0.5588235295 = 0.655691083 Reorder the terms: -0.5588235295 + x = 0.655691083 Solving -0.5588235295 + x = 0.655691083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5588235295' to each side of the equation. -0.5588235295 + 0.5588235295 + x = 0.655691083 + 0.5588235295 Combine like terms: -0.5588235295 + 0.5588235295 = 0.0000000000 0.0000000000 + x = 0.655691083 + 0.5588235295 x = 0.655691083 + 0.5588235295 Combine like terms: 0.655691083 + 0.5588235295 = 1.2145146125 x = 1.2145146125 Simplifying x = 1.2145146125

Subproblem 2

x + -0.5588235295 = -0.655691083 Simplifying x + -0.5588235295 = -0.655691083 Reorder the terms: -0.5588235295 + x = -0.655691083 Solving -0.5588235295 + x = -0.655691083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5588235295' to each side of the equation. -0.5588235295 + 0.5588235295 + x = -0.655691083 + 0.5588235295 Combine like terms: -0.5588235295 + 0.5588235295 = 0.0000000000 0.0000000000 + x = -0.655691083 + 0.5588235295 x = -0.655691083 + 0.5588235295 Combine like terms: -0.655691083 + 0.5588235295 = -0.0968675535 x = -0.0968675535 Simplifying x = -0.0968675535

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2145146125, -0.0968675535}

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