0=-4.9x^2+20x+1

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Solution for 0=-4.9x^2+20x+1 equation:


Simplifying
0 = -4.9x2 + 20x + 1

Reorder the terms:
0 = 1 + 20x + -4.9x2

Solving
0 = 1 + 20x + -4.9x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + -20x + 4.9x2 = 1 + 20x + -4.9x2 + -1 + -20x + 4.9x2

Reorder the terms:
-1 + -20x + 4.9x2 = 1 + -1 + 20x + -20x + -4.9x2 + 4.9x2

Combine like terms: 1 + -1 = 0
-1 + -20x + 4.9x2 = 0 + 20x + -20x + -4.9x2 + 4.9x2
-1 + -20x + 4.9x2 = 20x + -20x + -4.9x2 + 4.9x2

Combine like terms: 20x + -20x = 0
-1 + -20x + 4.9x2 = 0 + -4.9x2 + 4.9x2
-1 + -20x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-1 + -20x + 4.9x2 = 0.0

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

Divide each side by '4.9'.
-0.2040816327 + -4.081632653x + x2 = 0

Move the constant term to the right:

Add '0.2040816327' to each side of the equation.
-0.2040816327 + -4.081632653x + 0.2040816327 + x2 = 0 + 0.2040816327

Reorder the terms:
-0.2040816327 + 0.2040816327 + -4.081632653x + x2 = 0 + 0.2040816327

Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000
0.0000000000 + -4.081632653x + x2 = 0 + 0.2040816327
-4.081632653x + x2 = 0 + 0.2040816327

Combine like terms: 0 + 0.2040816327 = 0.2040816327
-4.081632653x + x2 = 0.2040816327

The x term is -4.081632653x.  Take half its coefficient (-2.040816327).
Square it (4.164931281) and add it to both sides.

Add '4.164931281' to each side of the equation.
-4.081632653x + 4.164931281 + x2 = 0.2040816327 + 4.164931281

Reorder the terms:
4.164931281 + -4.081632653x + x2 = 0.2040816327 + 4.164931281

Combine like terms: 0.2040816327 + 4.164931281 = 4.3690129137
4.164931281 + -4.081632653x + x2 = 4.3690129137

Factor a perfect square on the left side:
(x + -2.040816327)(x + -2.040816327) = 4.3690129137

Calculate the square root of the right side: 2.090218389

Break this problem into two subproblems by setting 
(x + -2.040816327) equal to 2.090218389 and -2.090218389.

Subproblem 1

x + -2.040816327 = 2.090218389 Simplifying x + -2.040816327 = 2.090218389 Reorder the terms: -2.040816327 + x = 2.090218389 Solving -2.040816327 + x = 2.090218389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = 2.090218389 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 2.090218389 + 2.040816327 x = 2.090218389 + 2.040816327 Combine like terms: 2.090218389 + 2.040816327 = 4.131034716 x = 4.131034716 Simplifying x = 4.131034716

Subproblem 2

x + -2.040816327 = -2.090218389 Simplifying x + -2.040816327 = -2.090218389 Reorder the terms: -2.040816327 + x = -2.090218389 Solving -2.040816327 + x = -2.090218389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = -2.090218389 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -2.090218389 + 2.040816327 x = -2.090218389 + 2.040816327 Combine like terms: -2.090218389 + 2.040816327 = -0.049402062 x = -0.049402062 Simplifying x = -0.049402062

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.131034716, -0.049402062}

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