(x+0.9)(x+1.8)=0

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Solution for (x+0.9)(x+1.8)=0 equation:


Simplifying
(x + 0.9)(x + 1.8) = 0

Reorder the terms:
(0.9 + x)(x + 1.8) = 0

Reorder the terms:
(0.9 + x)(1.8 + x) = 0

Multiply (0.9 + x) * (1.8 + x)
(0.9(1.8 + x) + x(1.8 + x)) = 0
((1.8 * 0.9 + x * 0.9) + x(1.8 + x)) = 0
((1.62 + 0.9x) + x(1.8 + x)) = 0
(1.62 + 0.9x + (1.8 * x + x * x)) = 0
(1.62 + 0.9x + (1.8x + x2)) = 0

Combine like terms: 0.9x + 1.8x = 2.7x
(1.62 + 2.7x + x2) = 0

Solving
1.62 + 2.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.62' to each side of the equation.
1.62 + 2.7x + -1.62 + x2 = 0 + -1.62

Reorder the terms:
1.62 + -1.62 + 2.7x + x2 = 0 + -1.62

Combine like terms: 1.62 + -1.62 = 0.00
0.00 + 2.7x + x2 = 0 + -1.62
2.7x + x2 = 0 + -1.62

Combine like terms: 0 + -1.62 = -1.62
2.7x + x2 = -1.62

The x term is 2.7x.  Take half its coefficient (1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
2.7x + 1.8225 + x2 = -1.62 + 1.8225

Reorder the terms:
1.8225 + 2.7x + x2 = -1.62 + 1.8225

Combine like terms: -1.62 + 1.8225 = 0.2025
1.8225 + 2.7x + x2 = 0.2025

Factor a perfect square on the left side:
(x + 1.35)(x + 1.35) = 0.2025

Calculate the square root of the right side: 0.45

Break this problem into two subproblems by setting 
(x + 1.35) equal to 0.45 and -0.45.

Subproblem 1

x + 1.35 = 0.45 Simplifying x + 1.35 = 0.45 Reorder the terms: 1.35 + x = 0.45 Solving 1.35 + x = 0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = 0.45 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = 0.45 + -1.35 x = 0.45 + -1.35 Combine like terms: 0.45 + -1.35 = -0.9 x = -0.9 Simplifying x = -0.9

Subproblem 2

x + 1.35 = -0.45 Simplifying x + 1.35 = -0.45 Reorder the terms: 1.35 + x = -0.45 Solving 1.35 + x = -0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = -0.45 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = -0.45 + -1.35 x = -0.45 + -1.35 Combine like terms: -0.45 + -1.35 = -1.8 x = -1.8 Simplifying x = -1.8

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.9, -1.8}

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