x^2-48x=-104

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Solution for x^2-48x=-104 equation:


Simplifying
x2 + -48x = -104

Reorder the terms:
-48x + x2 = -104

Solving
-48x + x2 = -104

Solving for variable 'x'.

Reorder the terms:
104 + -48x + x2 = -104 + 104

Combine like terms: -104 + 104 = 0
104 + -48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-104' to each side of the equation.
104 + -48x + -104 + x2 = 0 + -104

Reorder the terms:
104 + -104 + -48x + x2 = 0 + -104

Combine like terms: 104 + -104 = 0
0 + -48x + x2 = 0 + -104
-48x + x2 = 0 + -104

Combine like terms: 0 + -104 = -104
-48x + x2 = -104

The x term is -48x.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48x + 576 + x2 = -104 + 576

Reorder the terms:
576 + -48x + x2 = -104 + 576

Combine like terms: -104 + 576 = 472
576 + -48x + x2 = 472

Factor a perfect square on the left side:
(x + -24)(x + -24) = 472

Calculate the square root of the right side: 21.725560982

Break this problem into two subproblems by setting 
(x + -24) equal to 21.725560982 and -21.725560982.

Subproblem 1

x + -24 = 21.725560982 Simplifying x + -24 = 21.725560982 Reorder the terms: -24 + x = 21.725560982 Solving -24 + x = 21.725560982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 21.725560982 + 24 Combine like terms: -24 + 24 = 0 0 + x = 21.725560982 + 24 x = 21.725560982 + 24 Combine like terms: 21.725560982 + 24 = 45.725560982 x = 45.725560982 Simplifying x = 45.725560982

Subproblem 2

x + -24 = -21.725560982 Simplifying x + -24 = -21.725560982 Reorder the terms: -24 + x = -21.725560982 Solving -24 + x = -21.725560982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -21.725560982 + 24 Combine like terms: -24 + 24 = 0 0 + x = -21.725560982 + 24 x = -21.725560982 + 24 Combine like terms: -21.725560982 + 24 = 2.274439018 x = 2.274439018 Simplifying x = 2.274439018

Solution

The solution to the problem is based on the solutions from the subproblems. x = {45.725560982, 2.274439018}

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