X^2-100X+600=

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Solution for X^2-100X+600= equation:


Simplifying
X2 + -100X + 600 = 0

Reorder the terms:
600 + -100X + X2 = 0

Solving
600 + -100X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -100X + -600 + X2 = 0 + -600

Reorder the terms:
600 + -600 + -100X + X2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -100X + X2 = 0 + -600
-100X + X2 = 0 + -600

Combine like terms: 0 + -600 = -600
-100X + X2 = -600

The X term is -100X.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100X + 2500 + X2 = -600 + 2500

Reorder the terms:
2500 + -100X + X2 = -600 + 2500

Combine like terms: -600 + 2500 = 1900
2500 + -100X + X2 = 1900

Factor a perfect square on the left side:
(X + -50)(X + -50) = 1900

Calculate the square root of the right side: 43.588989435

Break this problem into two subproblems by setting 
(X + -50) equal to 43.588989435 and -43.588989435.

Subproblem 1

X + -50 = 43.588989435 Simplifying X + -50 = 43.588989435 Reorder the terms: -50 + X = 43.588989435 Solving -50 + X = 43.588989435 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + X = 43.588989435 + 50 Combine like terms: -50 + 50 = 0 0 + X = 43.588989435 + 50 X = 43.588989435 + 50 Combine like terms: 43.588989435 + 50 = 93.588989435 X = 93.588989435 Simplifying X = 93.588989435

Subproblem 2

X + -50 = -43.588989435 Simplifying X + -50 = -43.588989435 Reorder the terms: -50 + X = -43.588989435 Solving -50 + X = -43.588989435 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + X = -43.588989435 + 50 Combine like terms: -50 + 50 = 0 0 + X = -43.588989435 + 50 X = -43.588989435 + 50 Combine like terms: -43.588989435 + 50 = 6.411010565 X = 6.411010565 Simplifying X = 6.411010565

Solution

The solution to the problem is based on the solutions from the subproblems. X = {93.588989435, 6.411010565}

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