x^2-24x=-10

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Solution for x^2-24x=-10 equation: 


Simplifying
x2 + -24x = -10

Reorder the terms:
-24x + x2 = -10

Solving
-24x + x2 = -10

Solving for variable 'x'.

Reorder the terms:
10 + -24x + x2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -24x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -24x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -24x + x2 = 0 + -10
-24x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-24x + x2 = -10

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 = -10 + 144

Reorder the terms:
144 + -24x + x2 = -10 + 144

Combine like terms: -10 + 144 = 134
144 + -24x + x2 = 134

Factor a perfect square on the left side:
(x + -12)(x + -12) = 134

Calculate the square root of the right side: 11.575836903

Break this problem into two subproblems by setting 
(x + -12) equal to 11.575836903 and -11.575836903.


Subproblem 1
x + -12 = 11.575836903

Simplifying
x + -12 = 11.575836903

Reorder the terms:
-12 + x = 11.575836903

Solving
-12 + x = 11.575836903

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 = 11.575836903 + 12

Combine like terms: -12 + 12 = 0
0 + x = 11.575836903 + 12
x = 11.575836903 + 12

Combine like terms: 11.575836903 + 12 = 23.575836903
x = 23.575836903

Simplifying
x = 23.575836903


Subproblem 2
x + -12 = -11.575836903

Simplifying
x + -12 = -11.575836903

Reorder the terms:
-12 + x = -11.575836903

Solving
-12 + x = -11.575836903

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 = -11.575836903 + 12

Combine like terms: -12 + 12 = 0
0 + x = -11.575836903 + 12
x = -11.575836903 + 12

Combine like terms: -11.575836903 + 12 = 0.424163097
x = 0.424163097

Simplifying
x = 0.424163097


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.575836903, 0.424163097}

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