20x^2-101x+118=0

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Solution for 20x^2-101x+118=0 equation:


Simplifying
20x2 + -101x + 118 = 0

Reorder the terms:
118 + -101x + 20x2 = 0

Solving
118 + -101x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
5.9 + -5.05x + x2 = 0

Move the constant term to the right:

Add '-5.9' to each side of the equation.
5.9 + -5.05x + -5.9 + x2 = 0 + -5.9

Reorder the terms:
5.9 + -5.9 + -5.05x + x2 = 0 + -5.9

Combine like terms: 5.9 + -5.9 = 0.0
0.0 + -5.05x + x2 = 0 + -5.9
-5.05x + x2 = 0 + -5.9

Combine like terms: 0 + -5.9 = -5.9
-5.05x + x2 = -5.9

The x term is -5.05x.  Take half its coefficient (-2.525).
Square it (6.375625) and add it to both sides.

Add '6.375625' to each side of the equation.
-5.05x + 6.375625 + x2 = -5.9 + 6.375625

Reorder the terms:
6.375625 + -5.05x + x2 = -5.9 + 6.375625

Combine like terms: -5.9 + 6.375625 = 0.475625
6.375625 + -5.05x + x2 = 0.475625

Factor a perfect square on the left side:
(x + -2.525)(x + -2.525) = 0.475625

Calculate the square root of the right side: 0.689655711

Break this problem into two subproblems by setting 
(x + -2.525) equal to 0.689655711 and -0.689655711.

Subproblem 1

x + -2.525 = 0.689655711 Simplifying x + -2.525 = 0.689655711 Reorder the terms: -2.525 + x = 0.689655711 Solving -2.525 + x = 0.689655711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.525' to each side of the equation. -2.525 + 2.525 + x = 0.689655711 + 2.525 Combine like terms: -2.525 + 2.525 = 0.000 0.000 + x = 0.689655711 + 2.525 x = 0.689655711 + 2.525 Combine like terms: 0.689655711 + 2.525 = 3.214655711 x = 3.214655711 Simplifying x = 3.214655711

Subproblem 2

x + -2.525 = -0.689655711 Simplifying x + -2.525 = -0.689655711 Reorder the terms: -2.525 + x = -0.689655711 Solving -2.525 + x = -0.689655711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.525' to each side of the equation. -2.525 + 2.525 + x = -0.689655711 + 2.525 Combine like terms: -2.525 + 2.525 = 0.000 0.000 + x = -0.689655711 + 2.525 x = -0.689655711 + 2.525 Combine like terms: -0.689655711 + 2.525 = 1.835344289 x = 1.835344289 Simplifying x = 1.835344289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.214655711, 1.835344289}

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