x^2+18x-576=0

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Solution for x^2+18x-576=0 equation: 


Simplifying
x2 + 18x + -576 = 0

Reorder the terms:
-576 + 18x + x2 = 0

Solving
-576 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '576' to each side of the equation.
-576 + 18x + 576 + x2 = 0 + 576

Reorder the terms:
-576 + 576 + 18x + x2 = 0 + 576

Combine like terms: -576 + 576 = 0
0 + 18x + x2 = 0 + 576
18x + x2 = 0 + 576

Combine like terms: 0 + 576 = 576
18x + x2 = 576

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 = 576 + 81

Reorder the terms:
81 + 18x + x2 = 576 + 81

Combine like terms: 576 + 81 = 657
81 + 18x + x2 = 657

Factor a perfect square on the left side:
(x + 9)(x + 9) = 657

Calculate the square root of the right side: 25.632011236

Break this problem into two subproblems by setting 
(x + 9) equal to 25.632011236 and -25.632011236.


Subproblem 1
x + 9 = 25.632011236

Simplifying
x + 9 = 25.632011236

Reorder the terms:
9 + x = 25.632011236

Solving
9 + x = 25.632011236

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 = 25.632011236 + -9

Combine like terms: 9 + -9 = 0
0 + x = 25.632011236 + -9
x = 25.632011236 + -9

Combine like terms: 25.632011236 + -9 = 16.632011236
x = 16.632011236

Simplifying
x = 16.632011236


Subproblem 2
x + 9 = -25.632011236

Simplifying
x + 9 = -25.632011236

Reorder the terms:
9 + x = -25.632011236

Solving
9 + x = -25.632011236

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 = -25.632011236 + -9

Combine like terms: 9 + -9 = 0
0 + x = -25.632011236 + -9
x = -25.632011236 + -9

Combine like terms: -25.632011236 + -9 = -34.632011236
x = -34.632011236

Simplifying
x = -34.632011236


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.632011236, -34.632011236}

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