x^2-39x+361=0

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Solution for x^2-39x+361=0 equation:


Simplifying
x2 + -39x + 361 = 0

Reorder the terms:
361 + -39x + x2 = 0

Solving
361 + -39x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-361' to each side of the equation.
361 + -39x + -361 + x2 = 0 + -361

Reorder the terms:
361 + -361 + -39x + x2 = 0 + -361

Combine like terms: 361 + -361 = 0
0 + -39x + x2 = 0 + -361
-39x + x2 = 0 + -361

Combine like terms: 0 + -361 = -361
-39x + x2 = -361

The x term is -39x.  Take half its coefficient (-19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
-39x + 380.25 + x2 = -361 + 380.25

Reorder the terms:
380.25 + -39x + x2 = -361 + 380.25

Combine like terms: -361 + 380.25 = 19.25
380.25 + -39x + x2 = 19.25

Factor a perfect square on the left side:
(x + -19.5)(x + -19.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + -19.5) equal to 4.387482194 and -4.387482194.

Subproblem 1

x + -19.5 = 4.387482194 Simplifying x + -19.5 = 4.387482194 Reorder the terms: -19.5 + x = 4.387482194 Solving -19.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 4.387482194 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 4.387482194 + 19.5 x = 4.387482194 + 19.5 Combine like terms: 4.387482194 + 19.5 = 23.887482194 x = 23.887482194 Simplifying x = 23.887482194

Subproblem 2

x + -19.5 = -4.387482194 Simplifying x + -19.5 = -4.387482194 Reorder the terms: -19.5 + x = -4.387482194 Solving -19.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -4.387482194 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -4.387482194 + 19.5 x = -4.387482194 + 19.5 Combine like terms: -4.387482194 + 19.5 = 15.112517806 x = 15.112517806 Simplifying x = 15.112517806

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.887482194, 15.112517806}

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