0.4x^2-4x+8.4=0

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Solution for 0.4x^2-4x+8.4=0 equation:


Simplifying
0.4x2 + -4x + 8.4 = 0

Reorder the terms:
8.4 + -4x + 0.4x2 = 0

Solving
8.4 + -4x + 0.4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.4 the coefficient of the squared term: 

Divide each side by '0.4'.
21 + -10x + x2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -10x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -10x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -10x + x2 = 0 + -21
-10x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-10x + x2 = -21

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -21 + 25

Reorder the terms:
25 + -10x + x2 = -21 + 25

Combine like terms: -21 + 25 = 4
25 + -10x + x2 = 4

Factor a perfect square on the left side:
(x + -5)(x + -5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + -5) equal to 2 and -2.


Subproblem 1
x + -5 = 2

Simplifying
x + -5 = 2

Reorder the terms:
-5 + x = 2

Solving
-5 + x = 2

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 2 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2 + 5
x = 2 + 5

Combine like terms: 2 + 5 = 7
x = 7

Simplifying
x = 7


Subproblem 2
x + -5 = -2

Simplifying
x + -5 = -2

Reorder the terms:
-5 + x = -2

Solving
-5 + x = -2

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -2 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2 + 5
x = -2 + 5

Combine like terms: -2 + 5 = 3
x = 3

Simplifying
x = 3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7, 3}

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