(16x^2)+195x-87=0

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Solution for (16x^2)+195x-87=0 equation:


Simplifying
(16x2) + 195x + -87 = 0

Reorder the terms:
-87 + 195x + (16x2) = 0

Solving
-87 + 195x + (16x2) = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-5.4375 + 12.1875x + x2 = 0

Move the constant term to the right:

Add '5.4375' to each side of the equation.
-5.4375 + 12.1875x + 5.4375 + x2 = 0 + 5.4375

Reorder the terms:
-5.4375 + 5.4375 + 12.1875x + x2 = 0 + 5.4375

Combine like terms: -5.4375 + 5.4375 = 0.0000
0.0000 + 12.1875x + x2 = 0 + 5.4375
12.1875x + x2 = 0 + 5.4375

Combine like terms: 0 + 5.4375 = 5.4375
12.1875x + x2 = 5.4375

The x term is 12.1875x.  Take half its coefficient (6.09375).
Square it (37.13378906) and add it to both sides.

Add '37.13378906' to each side of the equation.
12.1875x + 37.13378906 + x2 = 5.4375 + 37.13378906

Reorder the terms:
37.13378906 + 12.1875x + x2 = 5.4375 + 37.13378906

Combine like terms: 5.4375 + 37.13378906 = 42.57128906
37.13378906 + 12.1875x + x2 = 42.57128906

Factor a perfect square on the left side:
((x) + 6.09375)((x) + 6.09375) = 42.57128906

Calculate the square root of the right side: 6.524667736

Break this problem into two subproblems by setting 
((x) + 6.09375) equal to 6.524667736 and -6.524667736.

Subproblem 1

(x) + 6.09375 = 6.524667736 Simplifying (x) + 6.09375 = 6.524667736 x + 6.09375 = 6.524667736 Reorder the terms: 6.09375 + x = 6.524667736 Solving 6.09375 + x = 6.524667736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.09375' to each side of the equation. 6.09375 + -6.09375 + x = 6.524667736 + -6.09375 Combine like terms: 6.09375 + -6.09375 = 0.00000 0.00000 + x = 6.524667736 + -6.09375 x = 6.524667736 + -6.09375 Combine like terms: 6.524667736 + -6.09375 = 0.430917736 x = 0.430917736 Simplifying x = 0.430917736

Subproblem 2

(x) + 6.09375 = -6.524667736 Simplifying (x) + 6.09375 = -6.524667736 x + 6.09375 = -6.524667736 Reorder the terms: 6.09375 + x = -6.524667736 Solving 6.09375 + x = -6.524667736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.09375' to each side of the equation. 6.09375 + -6.09375 + x = -6.524667736 + -6.09375 Combine like terms: 6.09375 + -6.09375 = 0.00000 0.00000 + x = -6.524667736 + -6.09375 x = -6.524667736 + -6.09375 Combine like terms: -6.524667736 + -6.09375 = -12.618417736 x = -12.618417736 Simplifying x = -12.618417736

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.430917736, -12.618417736}

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