244(x)=x^2-6x+28

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Solution for 244(x)=x^2-6x+28 equation:


Simplifying
244(x) = x2 + -6x + 28

Reorder the terms:
244x = 28 + -6x + x2

Solving
244x = 28 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-28 + 244x + 6x + -1x2 = 28 + -6x + x2 + -28 + 6x + -1x2

Combine like terms: 244x + 6x = 250x
-28 + 250x + -1x2 = 28 + -6x + x2 + -28 + 6x + -1x2

Reorder the terms:
-28 + 250x + -1x2 = 28 + -28 + -6x + 6x + x2 + -1x2

Combine like terms: 28 + -28 = 0
-28 + 250x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-28 + 250x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-28 + 250x + -1x2 = 0 + x2 + -1x2
-28 + 250x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + 250x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
28 + -250x + x2 = 0

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -250x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -250x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -250x + x2 = 0 + -28
-250x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-250x + x2 = -28

The x term is -250x.  Take half its coefficient (-125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
-250x + 15625 + x2 = -28 + 15625

Reorder the terms:
15625 + -250x + x2 = -28 + 15625

Combine like terms: -28 + 15625 = 15597
15625 + -250x + x2 = 15597

Factor a perfect square on the left side:
(x + -125)(x + -125) = 15597

Calculate the square root of the right side: 124.887949779

Break this problem into two subproblems by setting 
(x + -125) equal to 124.887949779 and -124.887949779.

Subproblem 1

x + -125 = 124.887949779 Simplifying x + -125 = 124.887949779 Reorder the terms: -125 + x = 124.887949779 Solving -125 + x = 124.887949779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 124.887949779 + 125 Combine like terms: -125 + 125 = 0 0 + x = 124.887949779 + 125 x = 124.887949779 + 125 Combine like terms: 124.887949779 + 125 = 249.887949779 x = 249.887949779 Simplifying x = 249.887949779

Subproblem 2

x + -125 = -124.887949779 Simplifying x + -125 = -124.887949779 Reorder the terms: -125 + x = -124.887949779 Solving -125 + x = -124.887949779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -124.887949779 + 125 Combine like terms: -125 + 125 = 0 0 + x = -124.887949779 + 125 x = -124.887949779 + 125 Combine like terms: -124.887949779 + 125 = 0.112050221 x = 0.112050221 Simplifying x = 0.112050221

Solution

The solution to the problem is based on the solutions from the subproblems. x = {249.887949779, 0.112050221}

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