x^2+39x+47=0

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Solution for x^2+39x+47=0 equation:


Simplifying
x2 + 39x + 47 = 0

Reorder the terms:
47 + 39x + x2 = 0

Solving
47 + 39x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 39x + -47 + x2 = 0 + -47

Reorder the terms:
47 + -47 + 39x + x2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 39x + x2 = 0 + -47
39x + x2 = 0 + -47

Combine like terms: 0 + -47 = -47
39x + x2 = -47

The x term is 39x.  Take half its coefficient (19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
39x + 380.25 + x2 = -47 + 380.25

Reorder the terms:
380.25 + 39x + x2 = -47 + 380.25

Combine like terms: -47 + 380.25 = 333.25
380.25 + 39x + x2 = 333.25

Factor a perfect square on the left side:
(x + 19.5)(x + 19.5) = 333.25

Calculate the square root of the right side: 18.255136264

Break this problem into two subproblems by setting 
(x + 19.5) equal to 18.255136264 and -18.255136264.

Subproblem 1

x + 19.5 = 18.255136264 Simplifying x + 19.5 = 18.255136264 Reorder the terms: 19.5 + x = 18.255136264 Solving 19.5 + x = 18.255136264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 18.255136264 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 18.255136264 + -19.5 x = 18.255136264 + -19.5 Combine like terms: 18.255136264 + -19.5 = -1.244863736 x = -1.244863736 Simplifying x = -1.244863736

Subproblem 2

x + 19.5 = -18.255136264 Simplifying x + 19.5 = -18.255136264 Reorder the terms: 19.5 + x = -18.255136264 Solving 19.5 + x = -18.255136264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -18.255136264 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -18.255136264 + -19.5 x = -18.255136264 + -19.5 Combine like terms: -18.255136264 + -19.5 = -37.755136264 x = -37.755136264 Simplifying x = -37.755136264

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.244863736, -37.755136264}

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