x^2-41x-400=0

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Solution for x^2-41x-400=0 equation:


Simplifying
x2 + -41x + -400 = 0

Reorder the terms:
-400 + -41x + x2 = 0

Solving
-400 + -41x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -41x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -41x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -41x + x2 = 0 + 400
-41x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-41x + x2 = 400

The x term is -41x.  Take half its coefficient (-20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
-41x + 420.25 + x2 = 400 + 420.25

Reorder the terms:
420.25 + -41x + x2 = 400 + 420.25

Combine like terms: 400 + 420.25 = 820.25
420.25 + -41x + x2 = 820.25

Factor a perfect square on the left side:
(x + -20.5)(x + -20.5) = 820.25

Calculate the square root of the right side: 28.640006983

Break this problem into two subproblems by setting 
(x + -20.5) equal to 28.640006983 and -28.640006983.

Subproblem 1

x + -20.5 = 28.640006983 Simplifying x + -20.5 = 28.640006983 Reorder the terms: -20.5 + x = 28.640006983 Solving -20.5 + x = 28.640006983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = 28.640006983 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = 28.640006983 + 20.5 x = 28.640006983 + 20.5 Combine like terms: 28.640006983 + 20.5 = 49.140006983 x = 49.140006983 Simplifying x = 49.140006983

Subproblem 2

x + -20.5 = -28.640006983 Simplifying x + -20.5 = -28.640006983 Reorder the terms: -20.5 + x = -28.640006983 Solving -20.5 + x = -28.640006983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = -28.640006983 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = -28.640006983 + 20.5 x = -28.640006983 + 20.5 Combine like terms: -28.640006983 + 20.5 = -8.140006983 x = -8.140006983 Simplifying x = -8.140006983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.140006983, -8.140006983}

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