x^2-18x+74=0

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Solution for x^2-18x+74=0 equation: 


Simplifying
x2 + -18x + 74 = 0

Reorder the terms:
74 + -18x + x2 = 0

Solving
74 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-74' to each side of the equation.
74 + -18x + -74 + x2 = 0 + -74

Reorder the terms:
74 + -74 + -18x + x2 = 0 + -74

Combine like terms: 74 + -74 = 0
0 + -18x + x2 = 0 + -74
-18x + x2 = 0 + -74

Combine like terms: 0 + -74 = -74
-18x + x2 = -74

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 = -74 + 81

Reorder the terms:
81 + -18x + x2 = -74 + 81

Combine like terms: -74 + 81 = 7
81 + -18x + x2 = 7

Factor a perfect square on the left side:
(x + -9)(x + -9) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -9) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + -9 = 2.645751311

Simplifying
x + -9 = 2.645751311

Reorder the terms:
-9 + x = 2.645751311

Solving
-9 + x = 2.645751311

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 = 2.645751311 + 9

Combine like terms: -9 + 9 = 0
0 + x = 2.645751311 + 9
x = 2.645751311 + 9

Combine like terms: 2.645751311 + 9 = 11.645751311
x = 11.645751311

Simplifying
x = 11.645751311


Subproblem 2
x + -9 = -2.645751311

Simplifying
x + -9 = -2.645751311

Reorder the terms:
-9 + x = -2.645751311

Solving
-9 + x = -2.645751311

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 = -2.645751311 + 9

Combine like terms: -9 + 9 = 0
0 + x = -2.645751311 + 9
x = -2.645751311 + 9

Combine like terms: -2.645751311 + 9 = 6.354248689
x = 6.354248689

Simplifying
x = 6.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.645751311, 6.354248689}

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