(x+2)(x+2)+3x=0

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Solution for (x+2)(x+2)+3x=0 equation:


Simplifying
(x + 2)(x + 2) + 3x = 0

Reorder the terms:
(2 + x)(x + 2) + 3x = 0

Reorder the terms:
(2 + x)(2 + x) + 3x = 0

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) + 3x = 0
((2 * 2 + x * 2) + x(2 + x)) + 3x = 0
((4 + 2x) + x(2 + x)) + 3x = 0
(4 + 2x + (2 * x + x * x)) + 3x = 0
(4 + 2x + (2x + x2)) + 3x = 0

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) + 3x = 0

Reorder the terms:
4 + 4x + 3x + x2 = 0

Combine like terms: 4x + 3x = 7x
4 + 7x + x2 = 0

Solving
4 + 7x + 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 + 7x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 7x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x + x2 = 0 + -4
7x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
7x + x2 = -4

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -4 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + 7x + x2 = 8.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

x + 3.5 = 2.872281323 Simplifying x + 3.5 = 2.872281323 Reorder the terms: 3.5 + x = 2.872281323 Solving 3.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.872281323 + -3.5 x = 2.872281323 + -3.5 Combine like terms: 2.872281323 + -3.5 = -0.627718677 x = -0.627718677 Simplifying x = -0.627718677

Subproblem 2

x + 3.5 = -2.872281323 Simplifying x + 3.5 = -2.872281323 Reorder the terms: 3.5 + x = -2.872281323 Solving 3.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.872281323 + -3.5 x = -2.872281323 + -3.5 Combine like terms: -2.872281323 + -3.5 = -6.372281323 x = -6.372281323 Simplifying x = -6.372281323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.627718677, -6.372281323}

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