-14x^2-5x-3x^2+2+11x=0

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Solution for -14x^2-5x-3x^2+2+11x=0 equation:


Simplifying
-14x2 + -5x + -3x2 + 2 + 11x = 0

Reorder the terms:
2 + -5x + 11x + -14x2 + -3x2 = 0

Combine like terms: -5x + 11x = 6x
2 + 6x + -14x2 + -3x2 = 0

Combine like terms: -14x2 + -3x2 = -17x2
2 + 6x + -17x2 = 0

Solving
2 + 6x + -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 + -0.3529411765x + x2 = 0

Move the constant term to the right:

Add '0.1176470588' to each side of the equation.
-0.1176470588 + -0.3529411765x + 0.1176470588 + x2 = 0 + 0.1176470588

Reorder the terms:
-0.1176470588 + 0.1176470588 + -0.3529411765x + x2 = 0 + 0.1176470588

Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000
0.0000000000 + -0.3529411765x + x2 = 0 + 0.1176470588
-0.3529411765x + x2 = 0 + 0.1176470588

Combine like terms: 0 + 0.1176470588 = 0.1176470588
-0.3529411765x + x2 = 0.1176470588

The x term is -0.3529411765x.  Take half its coefficient (-0.1764705883).
Square it (0.03114186853) and add it to both sides.

Add '0.03114186853' to each side of the equation.
-0.3529411765x + 0.03114186853 + x2 = 0.1176470588 + 0.03114186853

Reorder the terms:
0.03114186853 + -0.3529411765x + x2 = 0.1176470588 + 0.03114186853

Combine like terms: 0.1176470588 + 0.03114186853 = 0.14878892733
0.03114186853 + -0.3529411765x + x2 = 0.14878892733

Factor a perfect square on the left side:
(x + -0.1764705883)(x + -0.1764705883) = 0.14878892733

Calculate the square root of the right side: 0.385731678

Break this problem into two subproblems by setting 
(x + -0.1764705883) equal to 0.385731678 and -0.385731678.

Subproblem 1

x + -0.1764705883 = 0.385731678 Simplifying x + -0.1764705883 = 0.385731678 Reorder the terms: -0.1764705883 + x = 0.385731678 Solving -0.1764705883 + x = 0.385731678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + x = 0.385731678 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = 0.385731678 + 0.1764705883 x = 0.385731678 + 0.1764705883 Combine like terms: 0.385731678 + 0.1764705883 = 0.5622022663 x = 0.5622022663 Simplifying x = 0.5622022663

Subproblem 2

x + -0.1764705883 = -0.385731678 Simplifying x + -0.1764705883 = -0.385731678 Reorder the terms: -0.1764705883 + x = -0.385731678 Solving -0.1764705883 + x = -0.385731678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + x = -0.385731678 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = -0.385731678 + 0.1764705883 x = -0.385731678 + 0.1764705883 Combine like terms: -0.385731678 + 0.1764705883 = -0.2092610897 x = -0.2092610897 Simplifying x = -0.2092610897

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5622022663, -0.2092610897}

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