(x+0.2)(x+3.3)=0

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Solution for (x+0.2)(x+3.3)=0 equation:


Simplifying
(x + 0.2)(x + 3.3) = 0

Reorder the terms:
(0.2 + x)(x + 3.3) = 0

Reorder the terms:
(0.2 + x)(3.3 + x) = 0

Multiply (0.2 + x) * (3.3 + x)
(0.2(3.3 + x) + x(3.3 + x)) = 0
((3.3 * 0.2 + x * 0.2) + x(3.3 + x)) = 0
((0.66 + 0.2x) + x(3.3 + x)) = 0
(0.66 + 0.2x + (3.3 * x + x * x)) = 0
(0.66 + 0.2x + (3.3x + x2)) = 0

Combine like terms: 0.2x + 3.3x = 3.5x
(0.66 + 3.5x + x2) = 0

Solving
0.66 + 3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.66' to each side of the equation.
0.66 + 3.5x + -0.66 + x2 = 0 + -0.66

Reorder the terms:
0.66 + -0.66 + 3.5x + x2 = 0 + -0.66

Combine like terms: 0.66 + -0.66 = 0.00
0.00 + 3.5x + x2 = 0 + -0.66
3.5x + x2 = 0 + -0.66

Combine like terms: 0 + -0.66 = -0.66
3.5x + x2 = -0.66

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -0.66 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -0.66 + 3.0625

Combine like terms: -0.66 + 3.0625 = 2.4025
3.0625 + 3.5x + x2 = 2.4025

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 2.4025

Calculate the square root of the right side: 1.55

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.55 and -1.55.

Subproblem 1

x + 1.75 = 1.55 Simplifying x + 1.75 = 1.55 Reorder the terms: 1.75 + x = 1.55 Solving 1.75 + x = 1.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.55 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.55 + -1.75 x = 1.55 + -1.75 Combine like terms: 1.55 + -1.75 = -0.2 x = -0.2 Simplifying x = -0.2

Subproblem 2

x + 1.75 = -1.55 Simplifying x + 1.75 = -1.55 Reorder the terms: 1.75 + x = -1.55 Solving 1.75 + x = -1.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.55 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.55 + -1.75 x = -1.55 + -1.75 Combine like terms: -1.55 + -1.75 = -3.3 x = -3.3 Simplifying x = -3.3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -3.3}

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