x^2+10x-82=0

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Solution for x^2+10x-82=0 equation:


Simplifying
x2 + 10x + -82 = 0

Reorder the terms:
-82 + 10x + x2 = 0

Solving
-82 + 10x + 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 + 10x + 82 + x2 = 0 + 82

Reorder the terms:
-82 + 82 + 10x + x2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + 10x + x2 = 0 + 82
10x + x2 = 0 + 82

Combine like terms: 0 + 82 = 82
10x + x2 = 82

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 82 + 25

Reorder the terms:
25 + 10x + x2 = 82 + 25

Combine like terms: 82 + 25 = 107
25 + 10x + x2 = 107

Factor a perfect square on the left side:
(x + 5)(x + 5) = 107

Calculate the square root of the right side: 10.344080433

Break this problem into two subproblems by setting 
(x + 5) equal to 10.344080433 and -10.344080433.

Subproblem 1

x + 5 = 10.344080433 Simplifying x + 5 = 10.344080433 Reorder the terms: 5 + x = 10.344080433 Solving 5 + x = 10.344080433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 10.344080433 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.344080433 + -5 x = 10.344080433 + -5 Combine like terms: 10.344080433 + -5 = 5.344080433 x = 5.344080433 Simplifying x = 5.344080433

Subproblem 2

x + 5 = -10.344080433 Simplifying x + 5 = -10.344080433 Reorder the terms: 5 + x = -10.344080433 Solving 5 + x = -10.344080433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -10.344080433 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.344080433 + -5 x = -10.344080433 + -5 Combine like terms: -10.344080433 + -5 = -15.344080433 x = -15.344080433 Simplifying x = -15.344080433

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.344080433, -15.344080433}

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