x^2+31x+17=

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Solution for x^2+31x+17= equation:


Simplifying
x2 + 31x + 17 = 0

Reorder the terms:
17 + 31x + x2 = 0

Solving
17 + 31x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 31x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 31x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 31x + x2 = 0 + -17
31x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
31x + x2 = -17

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 = -17 + 240.25

Reorder the terms:
240.25 + 31x + x2 = -17 + 240.25

Combine like terms: -17 + 240.25 = 223.25
240.25 + 31x + x2 = 223.25

Factor a perfect square on the left side:
(x + 15.5)(x + 15.5) = 223.25

Calculate the square root of the right side: 14.941552797

Break this problem into two subproblems by setting 
(x + 15.5) equal to 14.941552797 and -14.941552797.

Subproblem 1

x + 15.5 = 14.941552797 Simplifying x + 15.5 = 14.941552797 Reorder the terms: 15.5 + x = 14.941552797 Solving 15.5 + x = 14.941552797 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 = 14.941552797 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 14.941552797 + -15.5 x = 14.941552797 + -15.5 Combine like terms: 14.941552797 + -15.5 = -0.558447203 x = -0.558447203 Simplifying x = -0.558447203

Subproblem 2

x + 15.5 = -14.941552797 Simplifying x + 15.5 = -14.941552797 Reorder the terms: 15.5 + x = -14.941552797 Solving 15.5 + x = -14.941552797 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 = -14.941552797 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -14.941552797 + -15.5 x = -14.941552797 + -15.5 Combine like terms: -14.941552797 + -15.5 = -30.441552797 x = -30.441552797 Simplifying x = -30.441552797

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.558447203, -30.441552797}

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