(6.4+x)*(5.6+x)=0

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Solution for (6.4+x)*(5.6+x)=0 equation:


Simplifying
(6.4 + x)(5.6 + x) = 0

Multiply (6.4 + x) * (5.6 + x)
(6.4(5.6 + x) + x(5.6 + x)) = 0
((5.6 * 6.4 + x * 6.4) + x(5.6 + x)) = 0
((35.84 + 6.4x) + x(5.6 + x)) = 0
(35.84 + 6.4x + (5.6 * x + x * x)) = 0
(35.84 + 6.4x + (5.6x + x2)) = 0

Combine like terms: 6.4x + 5.6x = 12x
(35.84 + 12x + x2) = 0

Solving
35.84 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-35.84' to each side of the equation.
35.84 + 12x + -35.84 + x2 = 0 + -35.84

Reorder the terms:
35.84 + -35.84 + 12x + x2 = 0 + -35.84

Combine like terms: 35.84 + -35.84 = 0.00
0.00 + 12x + x2 = 0 + -35.84
12x + x2 = 0 + -35.84

Combine like terms: 0 + -35.84 = -35.84
12x + x2 = -35.84

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -35.84 + 36

Reorder the terms:
36 + 12x + x2 = -35.84 + 36

Combine like terms: -35.84 + 36 = 0.16
36 + 12x + x2 = 0.16

Factor a perfect square on the left side:
(x + 6)(x + 6) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(x + 6) equal to 0.4 and -0.4.

Subproblem 1

x + 6 = 0.4 Simplifying x + 6 = 0.4 Reorder the terms: 6 + x = 0.4 Solving 6 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0.4 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0.4 + -6 x = 0.4 + -6 Combine like terms: 0.4 + -6 = -5.6 x = -5.6 Simplifying x = -5.6

Subproblem 2

x + 6 = -0.4 Simplifying x + 6 = -0.4 Reorder the terms: 6 + x = -0.4 Solving 6 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -0.4 + -6 Combine like terms: 6 + -6 = 0 0 + x = -0.4 + -6 x = -0.4 + -6 Combine like terms: -0.4 + -6 = -6.4 x = -6.4 Simplifying x = -6.4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.6, -6.4}

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