x^2+19x+65=0

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Solution for x^2+19x+65=0 equation:


Simplifying
x2 + 19x + 65 = 0

Reorder the terms:
65 + 19x + x2 = 0

Solving
65 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-65' to each side of the equation.
65 + 19x + -65 + x2 = 0 + -65

Reorder the terms:
65 + -65 + 19x + x2 = 0 + -65

Combine like terms: 65 + -65 = 0
0 + 19x + x2 = 0 + -65
19x + x2 = 0 + -65

Combine like terms: 0 + -65 = -65
19x + x2 = -65

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = -65 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -65 + 90.25

Combine like terms: -65 + 90.25 = 25.25
90.25 + 19x + x2 = 25.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + 9.5) equal to 5.024937811 and -5.024937811.

Subproblem 1

x + 9.5 = 5.024937811 Simplifying x + 9.5 = 5.024937811 Reorder the terms: 9.5 + x = 5.024937811 Solving 9.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 5.024937811 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 5.024937811 + -9.5 x = 5.024937811 + -9.5 Combine like terms: 5.024937811 + -9.5 = -4.475062189 x = -4.475062189 Simplifying x = -4.475062189

Subproblem 2

x + 9.5 = -5.024937811 Simplifying x + 9.5 = -5.024937811 Reorder the terms: 9.5 + x = -5.024937811 Solving 9.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -5.024937811 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -5.024937811 + -9.5 x = -5.024937811 + -9.5 Combine like terms: -5.024937811 + -9.5 = -14.524937811 x = -14.524937811 Simplifying x = -14.524937811

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.475062189, -14.524937811}

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