x^2-30x+82=0

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Solution for x^2-30x+82=0 equation:


Simplifying
x2 + -30x + 82 = 0

Reorder the terms:
82 + -30x + x2 = 0

Solving
82 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-82' to each side of the equation.
82 + -30x + -82 + x2 = 0 + -82

Reorder the terms:
82 + -82 + -30x + x2 = 0 + -82

Combine like terms: 82 + -82 = 0
0 + -30x + x2 = 0 + -82
-30x + x2 = 0 + -82

Combine like terms: 0 + -82 = -82
-30x + x2 = -82

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -82 + 225

Reorder the terms:
225 + -30x + x2 = -82 + 225

Combine like terms: -82 + 225 = 143
225 + -30x + x2 = 143

Factor a perfect square on the left side:
(x + -15)(x + -15) = 143

Calculate the square root of the right side: 11.958260743

Break this problem into two subproblems by setting 
(x + -15) equal to 11.958260743 and -11.958260743.

Subproblem 1

x + -15 = 11.958260743 Simplifying x + -15 = 11.958260743 Reorder the terms: -15 + x = 11.958260743 Solving -15 + x = 11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 11.958260743 + 15 Combine like terms: -15 + 15 = 0 0 + x = 11.958260743 + 15 x = 11.958260743 + 15 Combine like terms: 11.958260743 + 15 = 26.958260743 x = 26.958260743 Simplifying x = 26.958260743

Subproblem 2

x + -15 = -11.958260743 Simplifying x + -15 = -11.958260743 Reorder the terms: -15 + x = -11.958260743 Solving -15 + x = -11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -11.958260743 + 15 Combine like terms: -15 + 15 = 0 0 + x = -11.958260743 + 15 x = -11.958260743 + 15 Combine like terms: -11.958260743 + 15 = 3.041739257 x = 3.041739257 Simplifying x = 3.041739257

Solution

The solution to the problem is based on the solutions from the subproblems. x = {26.958260743, 3.041739257}

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