4.9x^2-9.8x-2=0

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Solution for 4.9x^2-9.8x-2=0 equation:


Simplifying
4.9x2 + -9.8x + -2 = 0

Reorder the terms:
-2 + -9.8x + 4.9x2 = 0

Solving
-2 + -9.8x + 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 + -2x + x2 = 0

Move the constant term to the right:

Add '0.4081632653' to each side of the equation.
-0.4081632653 + -2x + 0.4081632653 + x2 = 0 + 0.4081632653

Reorder the terms:
-0.4081632653 + 0.4081632653 + -2x + x2 = 0 + 0.4081632653

Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + 0.4081632653
-2x + x2 = 0 + 0.4081632653

Combine like terms: 0 + 0.4081632653 = 0.4081632653
-2x + x2 = 0.4081632653

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.4081632653 + 1

Reorder the terms:
1 + -2x + x2 = 0.4081632653 + 1

Combine like terms: 0.4081632653 + 1 = 1.4081632653
1 + -2x + x2 = 1.4081632653

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.4081632653

Calculate the square root of the right side: 1.186660552

Break this problem into two subproblems by setting 
(x + -1) equal to 1.186660552 and -1.186660552.

Subproblem 1

x + -1 = 1.186660552 Simplifying x + -1 = 1.186660552 Reorder the terms: -1 + x = 1.186660552 Solving -1 + x = 1.186660552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.186660552 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.186660552 + 1 x = 1.186660552 + 1 Combine like terms: 1.186660552 + 1 = 2.186660552 x = 2.186660552 Simplifying x = 2.186660552

Subproblem 2

x + -1 = -1.186660552 Simplifying x + -1 = -1.186660552 Reorder the terms: -1 + x = -1.186660552 Solving -1 + x = -1.186660552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.186660552 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.186660552 + 1 x = -1.186660552 + 1 Combine like terms: -1.186660552 + 1 = -0.186660552 x = -0.186660552 Simplifying x = -0.186660552

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.186660552, -0.186660552}

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