x^2-4x=24

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Solution for x^2-4x=24 equation:


Simplifying
x2 + -4x = 24

Reorder the terms:
-4x + x2 = 24

Solving
-4x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -4x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -4x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -4x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -4x + x2 = 0 + 24
-4x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-4x + x2 = 24

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 24 + 4

Reorder the terms:
4 + -4x + x2 = 24 + 4

Combine like terms: 24 + 4 = 28
4 + -4x + x2 = 28

Factor a perfect square on the left side:
(x + -2)(x + -2) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -2) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + -2 = 5.291502622 Simplifying x + -2 = 5.291502622 Reorder the terms: -2 + x = 5.291502622 Solving -2 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.291502622 + 2 x = 5.291502622 + 2 Combine like terms: 5.291502622 + 2 = 7.291502622 x = 7.291502622 Simplifying x = 7.291502622

Subproblem 2

x + -2 = -5.291502622 Simplifying x + -2 = -5.291502622 Reorder the terms: -2 + x = -5.291502622 Solving -2 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.291502622 + 2 x = -5.291502622 + 2 Combine like terms: -5.291502622 + 2 = -3.291502622 x = -3.291502622 Simplifying x = -3.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.291502622, -3.291502622}

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