x^2+18x=2

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


Simplifying
x2 + 18x = 2

Reorder the terms:
18x + x2 = 2

Solving
18x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 18x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 18x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 18x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 18x + x2 = 0 + 2
18x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
18x + x2 = 2

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 = 2 + 81

Reorder the terms:
81 + 18x + x2 = 2 + 81

Combine like terms: 2 + 81 = 83
81 + 18x + x2 = 83

Factor a perfect square on the left side:
(x + 9)(x + 9) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(x + 9) equal to 9.110433579 and -9.110433579.

Subproblem 1

x + 9 = 9.110433579 Simplifying x + 9 = 9.110433579 Reorder the terms: 9 + x = 9.110433579 Solving 9 + x = 9.110433579 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 = 9.110433579 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.110433579 + -9 x = 9.110433579 + -9 Combine like terms: 9.110433579 + -9 = 0.110433579 x = 0.110433579 Simplifying x = 0.110433579

Subproblem 2

x + 9 = -9.110433579 Simplifying x + 9 = -9.110433579 Reorder the terms: 9 + x = -9.110433579 Solving 9 + x = -9.110433579 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 = -9.110433579 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.110433579 + -9 x = -9.110433579 + -9 Combine like terms: -9.110433579 + -9 = -18.110433579 x = -18.110433579 Simplifying x = -18.110433579

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.110433579, -18.110433579}

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