1.8x^2-16x+28=0

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Solution for 1.8x^2-16x+28=0 equation:


Simplifying
1.8x2 + -16x + 28 = 0

Reorder the terms:
28 + -16x + 1.8x2 = 0

Solving
28 + -16x + 1.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.8'.
15.55555556 + -8.888888889x + x2 = 0

Move the constant term to the right:

Add '-15.55555556' to each side of the equation.
15.55555556 + -8.888888889x + -15.55555556 + x2 = 0 + -15.55555556

Reorder the terms:
15.55555556 + -15.55555556 + -8.888888889x + x2 = 0 + -15.55555556

Combine like terms: 15.55555556 + -15.55555556 = 0.00000000
0.00000000 + -8.888888889x + x2 = 0 + -15.55555556
-8.888888889x + x2 = 0 + -15.55555556

Combine like terms: 0 + -15.55555556 = -15.55555556
-8.888888889x + x2 = -15.55555556

The x term is -8.888888889x.  Take half its coefficient (-4.444444445).
Square it (19.75308642) and add it to both sides.

Add '19.75308642' to each side of the equation.
-8.888888889x + 19.75308642 + x2 = -15.55555556 + 19.75308642

Reorder the terms:
19.75308642 + -8.888888889x + x2 = -15.55555556 + 19.75308642

Combine like terms: -15.55555556 + 19.75308642 = 4.19753086
19.75308642 + -8.888888889x + x2 = 4.19753086

Factor a perfect square on the left side:
(x + -4.444444445)(x + -4.444444445) = 4.19753086

Calculate the square root of the right side: 2.048787656

Break this problem into two subproblems by setting 
(x + -4.444444445) equal to 2.048787656 and -2.048787656.

Subproblem 1

x + -4.444444445 = 2.048787656 Simplifying x + -4.444444445 = 2.048787656 Reorder the terms: -4.444444445 + x = 2.048787656 Solving -4.444444445 + x = 2.048787656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = 2.048787656 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = 2.048787656 + 4.444444445 x = 2.048787656 + 4.444444445 Combine like terms: 2.048787656 + 4.444444445 = 6.493232101 x = 6.493232101 Simplifying x = 6.493232101

Subproblem 2

x + -4.444444445 = -2.048787656 Simplifying x + -4.444444445 = -2.048787656 Reorder the terms: -4.444444445 + x = -2.048787656 Solving -4.444444445 + x = -2.048787656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = -2.048787656 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = -2.048787656 + 4.444444445 x = -2.048787656 + 4.444444445 Combine like terms: -2.048787656 + 4.444444445 = 2.395656789 x = 2.395656789 Simplifying x = 2.395656789

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.493232101, 2.395656789}

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