x^2+14x+19=0

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Solution for x^2+14x+19=0 equation:


Simplifying
x2 + 14x + 19 = 0

Reorder the terms:
19 + 14x + x2 = 0

Solving
19 + 14x + 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 + 14x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 14x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 14x + x2 = 0 + -19
14x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
14x + x2 = -19

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -19 + 49

Reorder the terms:
49 + 14x + x2 = -19 + 49

Combine like terms: -19 + 49 = 30
49 + 14x + x2 = 30

Factor a perfect square on the left side:
(x + 7)(x + 7) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 7) equal to 5.477225575 and -5.477225575.

Subproblem 1

x + 7 = 5.477225575 Simplifying x + 7 = 5.477225575 Reorder the terms: 7 + x = 5.477225575 Solving 7 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 5.477225575 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.477225575 + -7 x = 5.477225575 + -7 Combine like terms: 5.477225575 + -7 = -1.522774425 x = -1.522774425 Simplifying x = -1.522774425

Subproblem 2

x + 7 = -5.477225575 Simplifying x + 7 = -5.477225575 Reorder the terms: 7 + x = -5.477225575 Solving 7 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -5.477225575 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.477225575 + -7 x = -5.477225575 + -7 Combine like terms: -5.477225575 + -7 = -12.477225575 x = -12.477225575 Simplifying x = -12.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.522774425, -12.477225575}

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