x^2+18x+19=

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Solution for x^2+18x+19= equation:


Simplifying
x2 + 18x + 19 = 0

Reorder the terms:
19 + 18x + x2 = 0

Solving
19 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 18x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 18x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 18x + x2 = 0 + -19
18x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
18x + x2 = -19

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 = -19 + 81

Reorder the terms:
81 + 18x + x2 = -19 + 81

Combine like terms: -19 + 81 = 62
81 + 18x + x2 = 62

Factor a perfect square on the left side:
(x + 9)(x + 9) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(x + 9) equal to 7.874007874 and -7.874007874.

Subproblem 1

x + 9 = 7.874007874 Simplifying x + 9 = 7.874007874 Reorder the terms: 9 + x = 7.874007874 Solving 9 + x = 7.874007874 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 = 7.874007874 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.874007874 + -9 x = 7.874007874 + -9 Combine like terms: 7.874007874 + -9 = -1.125992126 x = -1.125992126 Simplifying x = -1.125992126

Subproblem 2

x + 9 = -7.874007874 Simplifying x + 9 = -7.874007874 Reorder the terms: 9 + x = -7.874007874 Solving 9 + x = -7.874007874 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 = -7.874007874 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.874007874 + -9 x = -7.874007874 + -9 Combine like terms: -7.874007874 + -9 = -16.874007874 x = -16.874007874 Simplifying x = -16.874007874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.125992126, -16.874007874}

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