x^2-28x+20=0

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Solution for x^2-28x+20=0 equation:


Simplifying
x2 + -28x + 20 = 0

Reorder the terms:
20 + -28x + x2 = 0

Solving
20 + -28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -28x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -28x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -28x + x2 = 0 + -20
-28x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-28x + x2 = -20

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = -20 + 196

Reorder the terms:
196 + -28x + x2 = -20 + 196

Combine like terms: -20 + 196 = 176
196 + -28x + x2 = 176

Factor a perfect square on the left side:
(x + -14)(x + -14) = 176

Calculate the square root of the right side: 13.266499161

Break this problem into two subproblems by setting 
(x + -14) equal to 13.266499161 and -13.266499161.

Subproblem 1

x + -14 = 13.266499161 Simplifying x + -14 = 13.266499161 Reorder the terms: -14 + x = 13.266499161 Solving -14 + x = 13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 13.266499161 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.266499161 + 14 x = 13.266499161 + 14 Combine like terms: 13.266499161 + 14 = 27.266499161 x = 27.266499161 Simplifying x = 27.266499161

Subproblem 2

x + -14 = -13.266499161 Simplifying x + -14 = -13.266499161 Reorder the terms: -14 + x = -13.266499161 Solving -14 + x = -13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -13.266499161 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.266499161 + 14 x = -13.266499161 + 14 Combine like terms: -13.266499161 + 14 = 0.733500839 x = 0.733500839 Simplifying x = 0.733500839

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.266499161, 0.733500839}

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