(x-2.1)(x+2.4)=

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Solution for (x-2.1)(x+2.4)= equation: 


Simplifying
(x + -2.1)(x + 2.4) = 0

Reorder the terms:
(-2.1 + x)(x + 2.4) = 0

Reorder the terms:
(-2.1 + x)(2.4 + x) = 0

Multiply (-2.1 + x) * (2.4 + x)
(-2.1(2.4 + x) + x(2.4 + x)) = 0
((2.4 * -2.1 + x * -2.1) + x(2.4 + x)) = 0
((-5.04 + -2.1x) + x(2.4 + x)) = 0
(-5.04 + -2.1x + (2.4 * x + x * x)) = 0
(-5.04 + -2.1x + (2.4x + x2)) = 0

Combine like terms: -2.1x + 2.4x = 0.3x
(-5.04 + 0.3x + x2) = 0

Solving
-5.04 + 0.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5.04' to each side of the equation.
-5.04 + 0.3x + 5.04 + x2 = 0 + 5.04

Reorder the terms:
-5.04 + 5.04 + 0.3x + x2 = 0 + 5.04

Combine like terms: -5.04 + 5.04 = 0.00
0.00 + 0.3x + x2 = 0 + 5.04
0.3x + x2 = 0 + 5.04

Combine like terms: 0 + 5.04 = 5.04
0.3x + x2 = 5.04

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 5.04 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 5.04 + 0.0225

Combine like terms: 5.04 + 0.0225 = 5.0625
0.0225 + 0.3x + x2 = 5.0625

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + 0.15) equal to 2.25 and -2.25.


Subproblem 1
x + 0.15 = 2.25

Simplifying
x + 0.15 = 2.25

Reorder the terms:
0.15 + x = 2.25

Solving
0.15 + x = 2.25

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 2.25 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 2.25 + -0.15
x = 2.25 + -0.15

Combine like terms: 2.25 + -0.15 = 2.1
x = 2.1

Simplifying
x = 2.1


Subproblem 2
x + 0.15 = -2.25

Simplifying
x + 0.15 = -2.25

Reorder the terms:
0.15 + x = -2.25

Solving
0.15 + x = -2.25

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -2.25 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -2.25 + -0.15
x = -2.25 + -0.15

Combine like terms: -2.25 + -0.15 = -2.4
x = -2.4

Simplifying
x = -2.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1, -2.4}

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