x^2+18x+53=0

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Solution for x^2+18x+53=0 equation:


Simplifying
x2 + 18x + 53 = 0

Reorder the terms:
53 + 18x + x2 = 0

Solving
53 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-53' to each side of the equation.
53 + 18x + -53 + x2 = 0 + -53

Reorder the terms:
53 + -53 + 18x + x2 = 0 + -53

Combine like terms: 53 + -53 = 0
0 + 18x + x2 = 0 + -53
18x + x2 = 0 + -53

Combine like terms: 0 + -53 = -53
18x + x2 = -53

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 = -53 + 81

Reorder the terms:
81 + 18x + x2 = -53 + 81

Combine like terms: -53 + 81 = 28
81 + 18x + x2 = 28

Factor a perfect square on the left side:
(x + 9)(x + 9) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + 9) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + 9 = 5.291502622 Simplifying x + 9 = 5.291502622 Reorder the terms: 9 + x = 5.291502622 Solving 9 + x = 5.291502622 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 = 5.291502622 + -9 Combine like terms: 9 + -9 = 0 0 + x = 5.291502622 + -9 x = 5.291502622 + -9 Combine like terms: 5.291502622 + -9 = -3.708497378 x = -3.708497378 Simplifying x = -3.708497378

Subproblem 2

x + 9 = -5.291502622 Simplifying x + 9 = -5.291502622 Reorder the terms: 9 + x = -5.291502622 Solving 9 + x = -5.291502622 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 = -5.291502622 + -9 Combine like terms: 9 + -9 = 0 0 + x = -5.291502622 + -9 x = -5.291502622 + -9 Combine like terms: -5.291502622 + -9 = -14.291502622 x = -14.291502622 Simplifying x = -14.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.708497378, -14.291502622}

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