x^2-2(x-2)=48

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Solution for x^2-2(x-2)=48 equation:


Simplifying
x2 + -2(x + -2) = 48

Reorder the terms:
x2 + -2(-2 + x) = 48
x2 + (-2 * -2 + x * -2) = 48
x2 + (4 + -2x) = 48

Reorder the terms:
4 + -2x + x2 = 48

Solving
4 + -2x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
4 + -48 + -2x + x2 = 48 + -48

Combine like terms: 4 + -48 = -44
-44 + -2x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-44 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -2x + 44 + x2 = 0 + 44

Reorder the terms:
-44 + 44 + -2x + x2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -2x + x2 = 0 + 44
-2x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
-2x + x2 = 44

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 = 44 + 1

Reorder the terms:
1 + -2x + x2 = 44 + 1

Combine like terms: 44 + 1 = 45
1 + -2x + x2 = 45

Factor a perfect square on the left side:
(x + -1)(x + -1) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -1) equal to 6.708203933 and -6.708203933.

Subproblem 1

x + -1 = 6.708203933 Simplifying x + -1 = 6.708203933 Reorder the terms: -1 + x = 6.708203933 Solving -1 + x = 6.708203933 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 = 6.708203933 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.708203933 + 1 x = 6.708203933 + 1 Combine like terms: 6.708203933 + 1 = 7.708203933 x = 7.708203933 Simplifying x = 7.708203933

Subproblem 2

x + -1 = -6.708203933 Simplifying x + -1 = -6.708203933 Reorder the terms: -1 + x = -6.708203933 Solving -1 + x = -6.708203933 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 = -6.708203933 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.708203933 + 1 x = -6.708203933 + 1 Combine like terms: -6.708203933 + 1 = -5.708203933 x = -5.708203933 Simplifying x = -5.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.708203933, -5.708203933}

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