4.9x^2-20x+2=0

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


Simplifying
4.9x2 + -20x + 2 = 0

Reorder the terms:
2 + -20x + 4.9x2 = 0

Solving
2 + -20x + 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 + -4.081632653x + x2 = 0

Move the constant term to the right:

Add '-0.4081632653' to each side of the equation.
0.4081632653 + -4.081632653x + -0.4081632653 + x2 = 0 + -0.4081632653

Reorder the terms:
0.4081632653 + -0.4081632653 + -4.081632653x + x2 = 0 + -0.4081632653

Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000
0.0000000000 + -4.081632653x + x2 = 0 + -0.4081632653
-4.081632653x + x2 = 0 + -0.4081632653

Combine like terms: 0 + -0.4081632653 = -0.4081632653
-4.081632653x + x2 = -0.4081632653

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 = -0.4081632653 + 4.164931281

Reorder the terms:
4.164931281 + -4.081632653x + x2 = -0.4081632653 + 4.164931281

Combine like terms: -0.4081632653 + 4.164931281 = 3.7567680157
4.164931281 + -4.081632653x + x2 = 3.7567680157

Factor a perfect square on the left side:
(x + -2.040816327)(x + -2.040816327) = 3.7567680157

Calculate the square root of the right side: 1.938238379

Break this problem into two subproblems by setting 
(x + -2.040816327) equal to 1.938238379 and -1.938238379.

Subproblem 1

x + -2.040816327 = 1.938238379 Simplifying x + -2.040816327 = 1.938238379 Reorder the terms: -2.040816327 + x = 1.938238379 Solving -2.040816327 + x = 1.938238379 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 = 1.938238379 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 1.938238379 + 2.040816327 x = 1.938238379 + 2.040816327 Combine like terms: 1.938238379 + 2.040816327 = 3.979054706 x = 3.979054706 Simplifying x = 3.979054706

Subproblem 2

x + -2.040816327 = -1.938238379 Simplifying x + -2.040816327 = -1.938238379 Reorder the terms: -2.040816327 + x = -1.938238379 Solving -2.040816327 + x = -1.938238379 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 = -1.938238379 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -1.938238379 + 2.040816327 x = -1.938238379 + 2.040816327 Combine like terms: -1.938238379 + 2.040816327 = 0.102577948 x = 0.102577948 Simplifying x = 0.102577948

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.979054706, 0.102577948}

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