x^2+18x+81=42

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Solution for x^2+18x+81=42 equation:


Simplifying
x2 + 18x + 81 = 42

Reorder the terms:
81 + 18x + x2 = 42

Solving
81 + 18x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
81 + -42 + 18x + x2 = 42 + -42

Combine like terms: 81 + -42 = 39
39 + 18x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
39 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 18x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + 18x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 18x + x2 = 0 + -39
18x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
18x + x2 = -39

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 = -39 + 81

Reorder the terms:
81 + 18x + x2 = -39 + 81

Combine like terms: -39 + 81 = 42
81 + 18x + x2 = 42

Factor a perfect square on the left side:
(x + 9)(x + 9) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(x + 9) equal to 6.480740698 and -6.480740698.

Subproblem 1

x + 9 = 6.480740698 Simplifying x + 9 = 6.480740698 Reorder the terms: 9 + x = 6.480740698 Solving 9 + x = 6.480740698 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 = 6.480740698 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.480740698 + -9 x = 6.480740698 + -9 Combine like terms: 6.480740698 + -9 = -2.519259302 x = -2.519259302 Simplifying x = -2.519259302

Subproblem 2

x + 9 = -6.480740698 Simplifying x + 9 = -6.480740698 Reorder the terms: 9 + x = -6.480740698 Solving 9 + x = -6.480740698 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 = -6.480740698 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.480740698 + -9 x = -6.480740698 + -9 Combine like terms: -6.480740698 + -9 = -15.480740698 x = -15.480740698 Simplifying x = -15.480740698

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.519259302, -15.480740698}

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