x^2+18x+75=0

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Solution for x^2+18x+75=0 equation:


Simplifying
x2 + 18x + 75 = 0

Reorder the terms:
75 + 18x + x2 = 0

Solving
75 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + 18x + -75 + x2 = 0 + -75

Reorder the terms:
75 + -75 + 18x + x2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + 18x + x2 = 0 + -75
18x + x2 = 0 + -75

Combine like terms: 0 + -75 = -75
18x + x2 = -75

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 = -75 + 81

Reorder the terms:
81 + 18x + x2 = -75 + 81

Combine like terms: -75 + 81 = 6
81 + 18x + x2 = 6

Factor a perfect square on the left side:
(x + 9)(x + 9) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 9) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + 9 = 2.449489743 Simplifying x + 9 = 2.449489743 Reorder the terms: 9 + x = 2.449489743 Solving 9 + x = 2.449489743 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 = 2.449489743 + -9 Combine like terms: 9 + -9 = 0 0 + x = 2.449489743 + -9 x = 2.449489743 + -9 Combine like terms: 2.449489743 + -9 = -6.550510257 x = -6.550510257 Simplifying x = -6.550510257

Subproblem 2

x + 9 = -2.449489743 Simplifying x + 9 = -2.449489743 Reorder the terms: 9 + x = -2.449489743 Solving 9 + x = -2.449489743 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 = -2.449489743 + -9 Combine like terms: 9 + -9 = 0 0 + x = -2.449489743 + -9 x = -2.449489743 + -9 Combine like terms: -2.449489743 + -9 = -11.449489743 x = -11.449489743 Simplifying x = -11.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-6.550510257, -11.449489743}

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