x^2-20x+83=0

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Solution for x^2-20x+83=0 equation:


Simplifying
x2 + -20x + 83 = 0

Reorder the terms:
83 + -20x + x2 = 0

Solving
83 + -20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-83' to each side of the equation.
83 + -20x + -83 + x2 = 0 + -83

Reorder the terms:
83 + -83 + -20x + x2 = 0 + -83

Combine like terms: 83 + -83 = 0
0 + -20x + x2 = 0 + -83
-20x + x2 = 0 + -83

Combine like terms: 0 + -83 = -83
-20x + x2 = -83

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 = -83 + 100

Reorder the terms:
100 + -20x + x2 = -83 + 100

Combine like terms: -83 + 100 = 17
100 + -20x + x2 = 17

Factor a perfect square on the left side:
(x + -10)(x + -10) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -10) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + -10 = 4.123105626 Simplifying x + -10 = 4.123105626 Reorder the terms: -10 + x = 4.123105626 Solving -10 + x = 4.123105626 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 = 4.123105626 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4.123105626 + 10 x = 4.123105626 + 10 Combine like terms: 4.123105626 + 10 = 14.123105626 x = 14.123105626 Simplifying x = 14.123105626

Subproblem 2

x + -10 = -4.123105626 Simplifying x + -10 = -4.123105626 Reorder the terms: -10 + x = -4.123105626 Solving -10 + x = -4.123105626 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 = -4.123105626 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4.123105626 + 10 x = -4.123105626 + 10 Combine like terms: -4.123105626 + 10 = 5.876894374 x = 5.876894374 Simplifying x = 5.876894374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.123105626, 5.876894374}

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