.33(x+2)(x+2)-5=22

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Solution for .33(x+2)(x+2)-5=22 equation:


Simplifying
0.33(x + 2)(x + 2) + -5 = 22

Reorder the terms:
0.33(2 + x)(x + 2) + -5 = 22

Reorder the terms:
0.33(2 + x)(2 + x) + -5 = 22

Multiply (2 + x) * (2 + x)
0.33(2(2 + x) + x(2 + x)) + -5 = 22
0.33((2 * 2 + x * 2) + x(2 + x)) + -5 = 22
0.33((4 + 2x) + x(2 + x)) + -5 = 22
0.33(4 + 2x + (2 * x + x * x)) + -5 = 22
0.33(4 + 2x + (2x + x2)) + -5 = 22

Combine like terms: 2x + 2x = 4x
0.33(4 + 4x + x2) + -5 = 22
(4 * 0.33 + 4x * 0.33 + x2 * 0.33) + -5 = 22
(1.32 + 1.32x + 0.33x2) + -5 = 22

Reorder the terms:
1.32 + -5 + 1.32x + 0.33x2 = 22

Combine like terms: 1.32 + -5 = -3.68
-3.68 + 1.32x + 0.33x2 = 22

Solving
-3.68 + 1.32x + 0.33x2 = 22

Solving for variable 'x'.

Reorder the terms:
-3.68 + -22 + 1.32x + 0.33x2 = 22 + -22

Combine like terms: -3.68 + -22 = -25.68
-25.68 + 1.32x + 0.33x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-25.68 + 1.32x + 0.33x2 = 0

Begin completing the square.  Divide all terms by
0.33 the coefficient of the squared term: 

Divide each side by '0.33'.
-77.81818182 + 4x + x2 = 0

Move the constant term to the right:

Add '77.81818182' to each side of the equation.
-77.81818182 + 4x + 77.81818182 + x2 = 0 + 77.81818182

Reorder the terms:
-77.81818182 + 77.81818182 + 4x + x2 = 0 + 77.81818182

Combine like terms: -77.81818182 + 77.81818182 = 0.00000000
0.00000000 + 4x + x2 = 0 + 77.81818182
4x + x2 = 0 + 77.81818182

Combine like terms: 0 + 77.81818182 = 77.81818182
4x + x2 = 77.81818182

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 77.81818182 + 4

Reorder the terms:
4 + 4x + x2 = 77.81818182 + 4

Combine like terms: 77.81818182 + 4 = 81.81818182
4 + 4x + x2 = 81.81818182

Factor a perfect square on the left side:
(x + 2)(x + 2) = 81.81818182

Calculate the square root of the right side: 9.045340337

Break this problem into two subproblems by setting 
(x + 2) equal to 9.045340337 and -9.045340337.

Subproblem 1

x + 2 = 9.045340337 Simplifying x + 2 = 9.045340337 Reorder the terms: 2 + x = 9.045340337 Solving 2 + x = 9.045340337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.045340337 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.045340337 + -2 x = 9.045340337 + -2 Combine like terms: 9.045340337 + -2 = 7.045340337 x = 7.045340337 Simplifying x = 7.045340337

Subproblem 2

x + 2 = -9.045340337 Simplifying x + 2 = -9.045340337 Reorder the terms: 2 + x = -9.045340337 Solving 2 + x = -9.045340337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.045340337 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.045340337 + -2 x = -9.045340337 + -2 Combine like terms: -9.045340337 + -2 = -11.045340337 x = -11.045340337 Simplifying x = -11.045340337

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.045340337, -11.045340337}

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