x*x+18x-81=0

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Solution for x*x+18x-81=0 equation:


Simplifying
x * x + 18x + -81 = 0

Multiply x * x
x2 + 18x + -81 = 0

Reorder the terms:
-81 + 18x + x2 = 0

Solving
-81 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 18x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + 18x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 18x + x2 = 0 + 81
18x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
18x + x2 = 81

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 = 81 + 81

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

Combine like terms: 81 + 81 = 162
81 + 18x + x2 = 162

Factor a perfect square on the left side:
(x + 9)(x + 9) = 162

Calculate the square root of the right side: 12.727922061

Break this problem into two subproblems by setting 
(x + 9) equal to 12.727922061 and -12.727922061.

Subproblem 1

x + 9 = 12.727922061 Simplifying x + 9 = 12.727922061 Reorder the terms: 9 + x = 12.727922061 Solving 9 + x = 12.727922061 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 = 12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.727922061 + -9 x = 12.727922061 + -9 Combine like terms: 12.727922061 + -9 = 3.727922061 x = 3.727922061 Simplifying x = 3.727922061

Subproblem 2

x + 9 = -12.727922061 Simplifying x + 9 = -12.727922061 Reorder the terms: 9 + x = -12.727922061 Solving 9 + x = -12.727922061 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 = -12.727922061 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.727922061 + -9 x = -12.727922061 + -9 Combine like terms: -12.727922061 + -9 = -21.727922061 x = -21.727922061 Simplifying x = -21.727922061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.727922061, -21.727922061}

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