x^2+13x+4=0

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Solution for x^2+13x+4=0 equation:


Simplifying
x2 + 13x + 4 = 0

Reorder the terms:
4 + 13x + x2 = 0

Solving
4 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 13x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 13x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 13x + x2 = 0 + -4
13x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
13x + x2 = -4

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -4 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -4 + 42.25

Combine like terms: -4 + 42.25 = 38.25
42.25 + 13x + x2 = 38.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

x + 6.5 = 6.184658438 Simplifying x + 6.5 = 6.184658438 Reorder the terms: 6.5 + x = 6.184658438 Solving 6.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 6.184658438 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.184658438 + -6.5 x = 6.184658438 + -6.5 Combine like terms: 6.184658438 + -6.5 = -0.315341562 x = -0.315341562 Simplifying x = -0.315341562

Subproblem 2

x + 6.5 = -6.184658438 Simplifying x + 6.5 = -6.184658438 Reorder the terms: 6.5 + x = -6.184658438 Solving 6.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -6.184658438 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.184658438 + -6.5 x = -6.184658438 + -6.5 Combine like terms: -6.184658438 + -6.5 = -12.684658438 x = -12.684658438 Simplifying x = -12.684658438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.315341562, -12.684658438}

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