x^2-18x+10=0

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Solution for x^2-18x+10=0 equation: 


Simplifying
x2 + -18x + 10 = 0

Reorder the terms:
10 + -18x + x2 = 0

Solving
10 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -18x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -18x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -18x + x2 = 0 + -10
-18x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-18x + x2 = -10

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -10 + 81

Reorder the terms:
81 + -18x + x2 = -10 + 81

Combine like terms: -10 + 81 = 71
81 + -18x + x2 = 71

Factor a perfect square on the left side:
(x + -9)(x + -9) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + -9) equal to 8.426149773 and -8.426149773.


Subproblem 1
x + -9 = 8.426149773

Simplifying
x + -9 = 8.426149773

Reorder the terms:
-9 + x = 8.426149773

Solving
-9 + x = 8.426149773

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + x = 8.426149773 + 9

Combine like terms: -9 + 9 = 0
0 + x = 8.426149773 + 9
x = 8.426149773 + 9

Combine like terms: 8.426149773 + 9 = 17.426149773
x = 17.426149773

Simplifying
x = 17.426149773


Subproblem 2
x + -9 = -8.426149773

Simplifying
x + -9 = -8.426149773

Reorder the terms:
-9 + x = -8.426149773

Solving
-9 + x = -8.426149773

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + x = -8.426149773 + 9

Combine like terms: -9 + 9 = 0
0 + x = -8.426149773 + 9
x = -8.426149773 + 9

Combine like terms: -8.426149773 + 9 = 0.573850227
x = 0.573850227

Simplifying
x = 0.573850227


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.426149773, 0.573850227}

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