x^2-2x=24+3

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Solution for x^2-2x=24+3 equation:


Simplifying
x2 + -2x = 24 + 3

Reorder the terms:
-2x + x2 = 24 + 3

Combine like terms: 24 + 3 = 27
-2x + x2 = 27

Solving
-2x + x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + -2x + x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -2x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -2x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2x + x2 = 0 + 27
-2x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-2x + x2 = 27

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 = 27 + 1

Reorder the terms:
1 + -2x + x2 = 27 + 1

Combine like terms: 27 + 1 = 28
1 + -2x + x2 = 28

Factor a perfect square on the left side:
(x + -1)(x + -1) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -1) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + -1 = 5.291502622 Simplifying x + -1 = 5.291502622 Reorder the terms: -1 + x = 5.291502622 Solving -1 + x = 5.291502622 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 = 5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.291502622 + 1 x = 5.291502622 + 1 Combine like terms: 5.291502622 + 1 = 6.291502622 x = 6.291502622 Simplifying x = 6.291502622

Subproblem 2

x + -1 = -5.291502622 Simplifying x + -1 = -5.291502622 Reorder the terms: -1 + x = -5.291502622 Solving -1 + x = -5.291502622 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 = -5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.291502622 + 1 x = -5.291502622 + 1 Combine like terms: -5.291502622 + 1 = -4.291502622 x = -4.291502622 Simplifying x = -4.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.291502622, -4.291502622}

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