-4.9x^2+196x+2=0

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Solution for -4.9x^2+196x+2=0 equation:


Simplifying
-4.9x2 + 196x + 2 = 0

Reorder the terms:
2 + 196x + -4.9x2 = 0

Solving
2 + 196x + -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 + -40x + x2 = 0

Move the constant term to the right:

Add '0.4081632653' to each side of the equation.
-0.4081632653 + -40x + 0.4081632653 + x2 = 0 + 0.4081632653

Reorder the terms:
-0.4081632653 + 0.4081632653 + -40x + x2 = 0 + 0.4081632653

Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000
0.0000000000 + -40x + x2 = 0 + 0.4081632653
-40x + x2 = 0 + 0.4081632653

Combine like terms: 0 + 0.4081632653 = 0.4081632653
-40x + x2 = 0.4081632653

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 0.4081632653 + 400

Reorder the terms:
400 + -40x + x2 = 0.4081632653 + 400

Combine like terms: 0.4081632653 + 400 = 400.4081632653
400 + -40x + x2 = 400.4081632653

Factor a perfect square on the left side:
(x + -20)(x + -20) = 400.4081632653

Calculate the square root of the right side: 20.01020148

Break this problem into two subproblems by setting 
(x + -20) equal to 20.01020148 and -20.01020148.

Subproblem 1

x + -20 = 20.01020148 Simplifying x + -20 = 20.01020148 Reorder the terms: -20 + x = 20.01020148 Solving -20 + x = 20.01020148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 20.01020148 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.01020148 + 20 x = 20.01020148 + 20 Combine like terms: 20.01020148 + 20 = 40.01020148 x = 40.01020148 Simplifying x = 40.01020148

Subproblem 2

x + -20 = -20.01020148 Simplifying x + -20 = -20.01020148 Reorder the terms: -20 + x = -20.01020148 Solving -20 + x = -20.01020148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -20.01020148 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.01020148 + 20 x = -20.01020148 + 20 Combine like terms: -20.01020148 + 20 = -0.01020148 x = -0.01020148 Simplifying x = -0.01020148

Solution

The solution to the problem is based on the solutions from the subproblems. x = {40.01020148, -0.01020148}

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