x^2-49x+200=0

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Solution for x^2-49x+200=0 equation:


Simplifying
x2 + -49x + 200 = 0

Reorder the terms:
200 + -49x + x2 = 0

Solving
200 + -49x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -49x + -200 + x2 = 0 + -200

Reorder the terms:
200 + -200 + -49x + x2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -49x + x2 = 0 + -200
-49x + x2 = 0 + -200

Combine like terms: 0 + -200 = -200
-49x + x2 = -200

The x term is -49x.  Take half its coefficient (-24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
-49x + 600.25 + x2 = -200 + 600.25

Reorder the terms:
600.25 + -49x + x2 = -200 + 600.25

Combine like terms: -200 + 600.25 = 400.25
600.25 + -49x + x2 = 400.25

Factor a perfect square on the left side:
(x + -24.5)(x + -24.5) = 400.25

Calculate the square root of the right side: 20.006249024

Break this problem into two subproblems by setting 
(x + -24.5) equal to 20.006249024 and -20.006249024.

Subproblem 1

x + -24.5 = 20.006249024 Simplifying x + -24.5 = 20.006249024 Reorder the terms: -24.5 + x = 20.006249024 Solving -24.5 + x = 20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 20.006249024 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 20.006249024 + 24.5 x = 20.006249024 + 24.5 Combine like terms: 20.006249024 + 24.5 = 44.506249024 x = 44.506249024 Simplifying x = 44.506249024

Subproblem 2

x + -24.5 = -20.006249024 Simplifying x + -24.5 = -20.006249024 Reorder the terms: -24.5 + x = -20.006249024 Solving -24.5 + x = -20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -20.006249024 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -20.006249024 + 24.5 x = -20.006249024 + 24.5 Combine like terms: -20.006249024 + 24.5 = 4.493750976 x = 4.493750976 Simplifying x = 4.493750976

Solution

The solution to the problem is based on the solutions from the subproblems. x = {44.506249024, 4.493750976}

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