52=x*x-2x

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Solution for 52=x*x-2x equation:


Simplifying
52 = x * x + -2x

Multiply x * x
52 = x2 + -2x

Reorder the terms:
52 = -2x + x2

Solving
52 = -2x + x2

Solving for variable 'x'.

Reorder the terms:
52 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
52 + 2x + -1x2 = 0 + x2 + -1x2
52 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
52 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-52 + -2x + x2 = 0

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + -2x + 52 + x2 = 0 + 52

Reorder the terms:
-52 + 52 + -2x + x2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -2x + x2 = 0 + 52
-2x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
-2x + x2 = 52

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 52 + 1

Reorder the terms:
1 + -2x + x2 = 52 + 1

Combine like terms: 52 + 1 = 53
1 + -2x + x2 = 53

Factor a perfect square on the left side:
(x + -1)(x + -1) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(x + -1) equal to 7.280109889 and -7.280109889.

Subproblem 1

x + -1 = 7.280109889 Simplifying x + -1 = 7.280109889 Reorder the terms: -1 + x = 7.280109889 Solving -1 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.280109889 + 1 x = 7.280109889 + 1 Combine like terms: 7.280109889 + 1 = 8.280109889 x = 8.280109889 Simplifying x = 8.280109889

Subproblem 2

x + -1 = -7.280109889 Simplifying x + -1 = -7.280109889 Reorder the terms: -1 + x = -7.280109889 Solving -1 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.280109889 + 1 x = -7.280109889 + 1 Combine like terms: -7.280109889 + 1 = -6.280109889 x = -6.280109889 Simplifying x = -6.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.280109889, -6.280109889}

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