2x=x^2-8x+1

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Solution for 2x=x^2-8x+1 equation:


Simplifying
2x = x2 + -8x + 1

Reorder the terms:
2x = 1 + -8x + x2

Solving
2x = 1 + -8x + x2

Solving for variable 'x'.

Reorder the terms:
-1 + 2x + 8x + -1x2 = 1 + -8x + x2 + -1 + 8x + -1x2

Combine like terms: 2x + 8x = 10x
-1 + 10x + -1x2 = 1 + -8x + x2 + -1 + 8x + -1x2

Reorder the terms:
-1 + 10x + -1x2 = 1 + -1 + -8x + 8x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-1 + 10x + -1x2 = 0 + -8x + 8x + x2 + -1x2
-1 + 10x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-1 + 10x + -1x2 = 0 + x2 + -1x2
-1 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + 10x + -1x2 = 0

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

Divide each side by '-1'.
1 + -10x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -10x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -10x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10x + x2 = 0 + -1
-10x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-10x + x2 = -1

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -1 + 25

Reorder the terms:
25 + -10x + x2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + -10x + x2 = 24

Factor a perfect square on the left side:
(x + -5)(x + -5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -5) equal to 4.898979486 and -4.898979486.

Subproblem 1

x + -5 = 4.898979486 Simplifying x + -5 = 4.898979486 Reorder the terms: -5 + x = 4.898979486 Solving -5 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.898979486 + 5 x = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 x = 9.898979486 Simplifying x = 9.898979486

Subproblem 2

x + -5 = -4.898979486 Simplifying x + -5 = -4.898979486 Reorder the terms: -5 + x = -4.898979486 Solving -5 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.898979486 + 5 x = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 x = 0.101020514 Simplifying x = 0.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.898979486, 0.101020514}

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