x^2+31x+13=

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Solution for x^2+31x+13= equation:


Simplifying
x2 + 31x + 13 = 0

Reorder the terms:
13 + 31x + x2 = 0

Solving
13 + 31x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 31x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + 31x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 31x + x2 = 0 + -13
31x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
31x + x2 = -13

The x term is 31x.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31x + 240.25 + x2 = -13 + 240.25

Reorder the terms:
240.25 + 31x + x2 = -13 + 240.25

Combine like terms: -13 + 240.25 = 227.25
240.25 + 31x + x2 = 227.25

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = 227.25

Calculate the square root of the right side: 15.074813432

Break this problem into two subproblems by setting 
(x + 15.5) equal to 15.074813432 and -15.074813432.

Subproblem 1

x + 15.5 = 15.074813432 Simplifying x + 15.5 = 15.074813432 Reorder the terms: 15.5 + x = 15.074813432 Solving 15.5 + x = 15.074813432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 15.074813432 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 15.074813432 + -15.5 x = 15.074813432 + -15.5 Combine like terms: 15.074813432 + -15.5 = -0.425186568 x = -0.425186568 Simplifying x = -0.425186568

Subproblem 2

x + 15.5 = -15.074813432 Simplifying x + 15.5 = -15.074813432 Reorder the terms: 15.5 + x = -15.074813432 Solving 15.5 + x = -15.074813432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -15.074813432 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -15.074813432 + -15.5 x = -15.074813432 + -15.5 Combine like terms: -15.074813432 + -15.5 = -30.574813432 x = -30.574813432 Simplifying x = -30.574813432

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.425186568, -30.574813432}

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