x^2-20x+6=0

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Solution for x^2-20x+6=0 equation:


Simplifying
x2 + -20x + 6 = 0

Reorder the terms:
6 + -20x + x2 = 0

Solving
6 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -20x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -20x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -20x + x2 = 0 + -6
-20x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-20x + x2 = -6

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -6 + 100

Reorder the terms:
100 + -20x + x2 = -6 + 100

Combine like terms: -6 + 100 = 94
100 + -20x + x2 = 94

Factor a perfect square on the left side:
(x + -10)(x + -10) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + -10) equal to 9.695359715 and -9.695359715.

Subproblem 1

x + -10 = 9.695359715 Simplifying x + -10 = 9.695359715 Reorder the terms: -10 + x = 9.695359715 Solving -10 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.695359715 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.695359715 + 10 x = 9.695359715 + 10 Combine like terms: 9.695359715 + 10 = 19.695359715 x = 19.695359715 Simplifying x = 19.695359715

Subproblem 2

x + -10 = -9.695359715 Simplifying x + -10 = -9.695359715 Reorder the terms: -10 + x = -9.695359715 Solving -10 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.695359715 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.695359715 + 10 x = -9.695359715 + 10 Combine like terms: -9.695359715 + 10 = 0.304640285 x = 0.304640285 Simplifying x = 0.304640285

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.695359715, 0.304640285}

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