(-1.2-x)(2.4-x)+4*.8=0

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Solution for (-1.2-x)(2.4-x)+4*.8=0 equation:


Simplifying
(-1.2 + -1x)(2.4 + -1x) + 4 * 0.8 = 0

Multiply (-1.2 + -1x) * (2.4 + -1x)
(-1.2(2.4 + -1x) + -1x * (2.4 + -1x)) + 4 * 0.8 = 0
((2.4 * -1.2 + -1x * -1.2) + -1x * (2.4 + -1x)) + 4 * 0.8 = 0
((-2.88 + 1.2x) + -1x * (2.4 + -1x)) + 4 * 0.8 = 0
(-2.88 + 1.2x + (2.4 * -1x + -1x * -1x)) + 4 * 0.8 = 0
(-2.88 + 1.2x + (-2.4x + 1x2)) + 4 * 0.8 = 0

Combine like terms: 1.2x + -2.4x = -1.2x
(-2.88 + -1.2x + 1x2) + 4 * 0.8 = 0

Multiply 4 * 0.8
-2.88 + -1.2x + 1x2 + 3.2 = 0

Reorder the terms:
-2.88 + 3.2 + -1.2x + 1x2 = 0

Combine like terms: -2.88 + 3.2 = 0.32
0.32 + -1.2x + 1x2 = 0

Solving
0.32 + -1.2x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.32' to each side of the equation.
0.32 + -1.2x + -0.32 + x2 = 0 + -0.32

Reorder the terms:
0.32 + -0.32 + -1.2x + x2 = 0 + -0.32

Combine like terms: 0.32 + -0.32 = 0.00
0.00 + -1.2x + x2 = 0 + -0.32
-1.2x + x2 = 0 + -0.32

Combine like terms: 0 + -0.32 = -0.32
-1.2x + x2 = -0.32

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = -0.32 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -0.32 + 0.36

Combine like terms: -0.32 + 0.36 = 0.04
0.36 + -1.2x + x2 = 0.04

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.2 and -0.2.

Subproblem 1

x + -0.6 = 0.2 Simplifying x + -0.6 = 0.2 Reorder the terms: -0.6 + x = 0.2 Solving -0.6 + x = 0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.2 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.2 + 0.6 x = 0.2 + 0.6 Combine like terms: 0.2 + 0.6 = 0.8 x = 0.8 Simplifying x = 0.8

Subproblem 2

x + -0.6 = -0.2 Simplifying x + -0.6 = -0.2 Reorder the terms: -0.6 + x = -0.2 Solving -0.6 + x = -0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.2 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.2 + 0.6 x = -0.2 + 0.6 Combine like terms: -0.2 + 0.6 = 0.4 x = 0.4 Simplifying x = 0.4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8, 0.4}

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