x^2-24x+92=0

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Solution for x^2-24x+92=0 equation:


Simplifying
x2 + -24x + 92 = 0

Reorder the terms:
92 + -24x + x2 = 0

Solving
92 + -24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-92' to each side of the equation.
92 + -24x + -92 + x2 = 0 + -92

Reorder the terms:
92 + -92 + -24x + x2 = 0 + -92

Combine like terms: 92 + -92 = 0
0 + -24x + x2 = 0 + -92
-24x + x2 = 0 + -92

Combine like terms: 0 + -92 = -92
-24x + x2 = -92

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -92 + 144

Reorder the terms:
144 + -24x + x2 = -92 + 144

Combine like terms: -92 + 144 = 52
144 + -24x + x2 = 52

Factor a perfect square on the left side:
(x + -12)(x + -12) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -12) equal to 7.211102551 and -7.211102551.

Subproblem 1

x + -12 = 7.211102551 Simplifying x + -12 = 7.211102551 Reorder the terms: -12 + x = 7.211102551 Solving -12 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 7.211102551 + 12 Combine like terms: -12 + 12 = 0 0 + x = 7.211102551 + 12 x = 7.211102551 + 12 Combine like terms: 7.211102551 + 12 = 19.211102551 x = 19.211102551 Simplifying x = 19.211102551

Subproblem 2

x + -12 = -7.211102551 Simplifying x + -12 = -7.211102551 Reorder the terms: -12 + x = -7.211102551 Solving -12 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -7.211102551 + 12 Combine like terms: -12 + 12 = 0 0 + x = -7.211102551 + 12 x = -7.211102551 + 12 Combine like terms: -7.211102551 + 12 = 4.788897449 x = 4.788897449 Simplifying x = 4.788897449

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.211102551, 4.788897449}

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