-4.9x^2-180x-2=0

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Solution for -4.9x^2-180x-2=0 equation:


Simplifying
-4.9x2 + -180x + -2 = 0

Reorder the terms:
-2 + -180x + -4.9x2 = 0

Solving
-2 + -180x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
0.4081632653 + 36.73469388x + x2 = 0

Move the constant term to the right:

Add '-0.4081632653' to each side of the equation.
0.4081632653 + 36.73469388x + -0.4081632653 + x2 = 0 + -0.4081632653

Reorder the terms:
0.4081632653 + -0.4081632653 + 36.73469388x + x2 = 0 + -0.4081632653

Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000
0.0000000000 + 36.73469388x + x2 = 0 + -0.4081632653
36.73469388x + x2 = 0 + -0.4081632653

Combine like terms: 0 + -0.4081632653 = -0.4081632653
36.73469388x + x2 = -0.4081632653

The x term is 36.73469388x.  Take half its coefficient (18.36734694).
Square it (337.3594336) and add it to both sides.

Add '337.3594336' to each side of the equation.
36.73469388x + 337.3594336 + x2 = -0.4081632653 + 337.3594336

Reorder the terms:
337.3594336 + 36.73469388x + x2 = -0.4081632653 + 337.3594336

Combine like terms: -0.4081632653 + 337.3594336 = 336.9512703347
337.3594336 + 36.73469388x + x2 = 336.9512703347

Factor a perfect square on the left side:
(x + 18.36734694)(x + 18.36734694) = 336.9512703347

Calculate the square root of the right side: 18.356232466

Break this problem into two subproblems by setting 
(x + 18.36734694) equal to 18.356232466 and -18.356232466.

Subproblem 1

x + 18.36734694 = 18.356232466 Simplifying x + 18.36734694 = 18.356232466 Reorder the terms: 18.36734694 + x = 18.356232466 Solving 18.36734694 + x = 18.356232466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.36734694' to each side of the equation. 18.36734694 + -18.36734694 + x = 18.356232466 + -18.36734694 Combine like terms: 18.36734694 + -18.36734694 = 0.00000000 0.00000000 + x = 18.356232466 + -18.36734694 x = 18.356232466 + -18.36734694 Combine like terms: 18.356232466 + -18.36734694 = -0.011114474 x = -0.011114474 Simplifying x = -0.011114474

Subproblem 2

x + 18.36734694 = -18.356232466 Simplifying x + 18.36734694 = -18.356232466 Reorder the terms: 18.36734694 + x = -18.356232466 Solving 18.36734694 + x = -18.356232466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.36734694' to each side of the equation. 18.36734694 + -18.36734694 + x = -18.356232466 + -18.36734694 Combine like terms: 18.36734694 + -18.36734694 = 0.00000000 0.00000000 + x = -18.356232466 + -18.36734694 x = -18.356232466 + -18.36734694 Combine like terms: -18.356232466 + -18.36734694 = -36.723579406 x = -36.723579406 Simplifying x = -36.723579406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.011114474, -36.723579406}

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