x^2-18x+74=13

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Solution for x^2-18x+74=13 equation:


Simplifying
x2 + -18x + 74 = 13

Reorder the terms:
74 + -18x + x2 = 13

Solving
74 + -18x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
74 + -13 + -18x + x2 = 13 + -13

Combine like terms: 74 + -13 = 61
61 + -18x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
61 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-61' to each side of the equation.
61 + -18x + -61 + x2 = 0 + -61

Reorder the terms:
61 + -61 + -18x + x2 = 0 + -61

Combine like terms: 61 + -61 = 0
0 + -18x + x2 = 0 + -61
-18x + x2 = 0 + -61

Combine like terms: 0 + -61 = -61
-18x + x2 = -61

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 = -61 + 81

Reorder the terms:
81 + -18x + x2 = -61 + 81

Combine like terms: -61 + 81 = 20
81 + -18x + x2 = 20

Factor a perfect square on the left side:
(x + -9)(x + -9) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -9) equal to 4.472135955 and -4.472135955.

Subproblem 1

x + -9 = 4.472135955 Simplifying x + -9 = 4.472135955 Reorder the terms: -9 + x = 4.472135955 Solving -9 + x = 4.472135955 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 = 4.472135955 + 9 Combine like terms: -9 + 9 = 0 0 + x = 4.472135955 + 9 x = 4.472135955 + 9 Combine like terms: 4.472135955 + 9 = 13.472135955 x = 13.472135955 Simplifying x = 13.472135955

Subproblem 2

x + -9 = -4.472135955 Simplifying x + -9 = -4.472135955 Reorder the terms: -9 + x = -4.472135955 Solving -9 + x = -4.472135955 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 = -4.472135955 + 9 Combine like terms: -9 + 9 = 0 0 + x = -4.472135955 + 9 x = -4.472135955 + 9 Combine like terms: -4.472135955 + 9 = 4.527864045 x = 4.527864045 Simplifying x = 4.527864045

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.472135955, 4.527864045}

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