x^2+4x=31-2x

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Solution for x^2+4x=31-2x equation:


Simplifying
x2 + 4x = 31 + -2x

Reorder the terms:
4x + x2 = 31 + -2x

Solving
4x + x2 = 31 + -2x

Solving for variable 'x'.

Reorder the terms:
-31 + 4x + 2x + x2 = 31 + -2x + -31 + 2x

Combine like terms: 4x + 2x = 6x
-31 + 6x + x2 = 31 + -2x + -31 + 2x

Reorder the terms:
-31 + 6x + x2 = 31 + -31 + -2x + 2x

Combine like terms: 31 + -31 = 0
-31 + 6x + x2 = 0 + -2x + 2x
-31 + 6x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-31 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 6x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 6x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 6x + x2 = 0 + 31
6x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
6x + x2 = 31

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 31 + 9

Reorder the terms:
9 + 6x + x2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + 6x + x2 = 40

Factor a perfect square on the left side:
(x + 3)(x + 3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 3) equal to 6.32455532 and -6.32455532.

Subproblem 1

x + 3 = 6.32455532 Simplifying x + 3 = 6.32455532 Reorder the terms: 3 + x = 6.32455532 Solving 3 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.32455532 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.32455532 + -3 x = 6.32455532 + -3 Combine like terms: 6.32455532 + -3 = 3.32455532 x = 3.32455532 Simplifying x = 3.32455532

Subproblem 2

x + 3 = -6.32455532 Simplifying x + 3 = -6.32455532 Reorder the terms: 3 + x = -6.32455532 Solving 3 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.32455532 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.32455532 + -3 x = -6.32455532 + -3 Combine like terms: -6.32455532 + -3 = -9.32455532 x = -9.32455532 Simplifying x = -9.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.32455532, -9.32455532}

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