19x^2-152x-9=0

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Solution for 19x^2-152x-9=0 equation:


Simplifying
19x2 + -152x + -9 = 0

Reorder the terms:
-9 + -152x + 19x2 = 0

Solving
-9 + -152x + 19x2 = 0

Solving for variable 'x'.

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

Divide each side by '19'.
-0.4736842105 + -8x + x2 = 0

Move the constant term to the right:

Add '0.4736842105' to each side of the equation.
-0.4736842105 + -8x + 0.4736842105 + x2 = 0 + 0.4736842105

Reorder the terms:
-0.4736842105 + 0.4736842105 + -8x + x2 = 0 + 0.4736842105

Combine like terms: -0.4736842105 + 0.4736842105 = 0.0000000000
0.0000000000 + -8x + x2 = 0 + 0.4736842105
-8x + x2 = 0 + 0.4736842105

Combine like terms: 0 + 0.4736842105 = 0.4736842105
-8x + x2 = 0.4736842105

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 0.4736842105 + 16

Reorder the terms:
16 + -8x + x2 = 0.4736842105 + 16

Combine like terms: 0.4736842105 + 16 = 16.4736842105
16 + -8x + x2 = 16.4736842105

Factor a perfect square on the left side:
(x + -4)(x + -4) = 16.4736842105

Calculate the square root of the right side: 4.05877866

Break this problem into two subproblems by setting 
(x + -4) equal to 4.05877866 and -4.05877866.

Subproblem 1

x + -4 = 4.05877866 Simplifying x + -4 = 4.05877866 Reorder the terms: -4 + x = 4.05877866 Solving -4 + x = 4.05877866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.05877866 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.05877866 + 4 x = 4.05877866 + 4 Combine like terms: 4.05877866 + 4 = 8.05877866 x = 8.05877866 Simplifying x = 8.05877866

Subproblem 2

x + -4 = -4.05877866 Simplifying x + -4 = -4.05877866 Reorder the terms: -4 + x = -4.05877866 Solving -4 + x = -4.05877866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.05877866 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.05877866 + 4 x = -4.05877866 + 4 Combine like terms: -4.05877866 + 4 = -0.05877866 x = -0.05877866 Simplifying x = -0.05877866

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.05877866, -0.05877866}

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