(x-2.7)(x+2.9)=

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Solution for (x-2.7)(x+2.9)= equation: 


Simplifying
(x + -2.7)(x + 2.9) = 0

Reorder the terms:
(-2.7 + x)(x + 2.9) = 0

Reorder the terms:
(-2.7 + x)(2.9 + x) = 0

Multiply (-2.7 + x) * (2.9 + x)
(-2.7(2.9 + x) + x(2.9 + x)) = 0
((2.9 * -2.7 + x * -2.7) + x(2.9 + x)) = 0
((-7.83 + -2.7x) + x(2.9 + x)) = 0
(-7.83 + -2.7x + (2.9 * x + x * x)) = 0
(-7.83 + -2.7x + (2.9x + x2)) = 0

Combine like terms: -2.7x + 2.9x = 0.2x
(-7.83 + 0.2x + x2) = 0

Solving
-7.83 + 0.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7.83' to each side of the equation.
-7.83 + 0.2x + 7.83 + x2 = 0 + 7.83

Reorder the terms:
-7.83 + 7.83 + 0.2x + x2 = 0 + 7.83

Combine like terms: -7.83 + 7.83 = 0.00
0.00 + 0.2x + x2 = 0 + 7.83
0.2x + x2 = 0 + 7.83

Combine like terms: 0 + 7.83 = 7.83
0.2x + x2 = 7.83

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 7.83 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 7.83 + 0.01

Combine like terms: 7.83 + 0.01 = 7.84
0.01 + 0.2x + x2 = 7.84

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 7.84

Calculate the square root of the right side: 2.8

Break this problem into two subproblems by setting 
(x + 0.1) equal to 2.8 and -2.8.


Subproblem 1
x + 0.1 = 2.8

Simplifying
x + 0.1 = 2.8

Reorder the terms:
0.1 + x = 2.8

Solving
0.1 + x = 2.8

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = 2.8 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = 2.8 + -0.1
x = 2.8 + -0.1

Combine like terms: 2.8 + -0.1 = 2.7
x = 2.7

Simplifying
x = 2.7


Subproblem 2
x + 0.1 = -2.8

Simplifying
x + 0.1 = -2.8

Reorder the terms:
0.1 + x = -2.8

Solving
0.1 + x = -2.8

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = -2.8 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = -2.8 + -0.1
x = -2.8 + -0.1

Combine like terms: -2.8 + -0.1 = -2.9
x = -2.9

Simplifying
x = -2.9


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.7, -2.9}

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