x^2+18x+81=5

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Solution for x^2+18x+81=5 equation:


Simplifying
x2 + 18x + 81 = 5

Reorder the terms:
81 + 18x + x2 = 5

Solving
81 + 18x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
81 + -5 + 18x + x2 = 5 + -5

Combine like terms: 81 + -5 = 76
76 + 18x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
76 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-76' to each side of the equation.
76 + 18x + -76 + x2 = 0 + -76

Reorder the terms:
76 + -76 + 18x + x2 = 0 + -76

Combine like terms: 76 + -76 = 0
0 + 18x + x2 = 0 + -76
18x + x2 = 0 + -76

Combine like terms: 0 + -76 = -76
18x + x2 = -76

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 = -76 + 81

Reorder the terms:
81 + 18x + x2 = -76 + 81

Combine like terms: -76 + 81 = 5
81 + 18x + x2 = 5

Factor a perfect square on the left side:
(x + 9)(x + 9) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 9) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + 9 = 2.236067978 Simplifying x + 9 = 2.236067978 Reorder the terms: 9 + x = 2.236067978 Solving 9 + x = 2.236067978 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 = 2.236067978 + -9 Combine like terms: 9 + -9 = 0 0 + x = 2.236067978 + -9 x = 2.236067978 + -9 Combine like terms: 2.236067978 + -9 = -6.763932022 x = -6.763932022 Simplifying x = -6.763932022

Subproblem 2

x + 9 = -2.236067978 Simplifying x + 9 = -2.236067978 Reorder the terms: 9 + x = -2.236067978 Solving 9 + x = -2.236067978 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 = -2.236067978 + -9 Combine like terms: 9 + -9 = 0 0 + x = -2.236067978 + -9 x = -2.236067978 + -9 Combine like terms: -2.236067978 + -9 = -11.236067978 x = -11.236067978 Simplifying x = -11.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-6.763932022, -11.236067978}

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