1.2x^2=2.1x+1.7

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Solution for 1.2x^2=2.1x+1.7 equation: 


Simplifying
1.2x2 = 2.1x + 1.7

Reorder the terms:
1.2x2 = 1.7 + 2.1x

Solving
1.2x2 = 1.7 + 2.1x

Solving for variable 'x'.

Reorder the terms:
-1.7 + -2.1x + 1.2x2 = 1.7 + 2.1x + -1.7 + -2.1x

Reorder the terms:
-1.7 + -2.1x + 1.2x2 = 1.7 + -1.7 + 2.1x + -2.1x

Combine like terms: 1.7 + -1.7 = 0.0
-1.7 + -2.1x + 1.2x2 = 0.0 + 2.1x + -2.1x
-1.7 + -2.1x + 1.2x2 = 2.1x + -2.1x

Combine like terms: 2.1x + -2.1x = 0.0
-1.7 + -2.1x + 1.2x2 = 0.0

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

Divide each side by '1.2'.
-1.416666667 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1.416666667' to each side of the equation.
-1.416666667 + -1.75x + 1.416666667 + x2 = 0 + 1.416666667

Reorder the terms:
-1.416666667 + 1.416666667 + -1.75x + x2 = 0 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + -1.75x + x2 = 0 + 1.416666667
-1.75x + x2 = 0 + 1.416666667

Combine like terms: 0 + 1.416666667 = 1.416666667
-1.75x + x2 = 1.416666667

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 1.416666667 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1.416666667 + 0.765625

Combine like terms: 1.416666667 + 0.765625 = 2.182291667
0.765625 + -1.75x + x2 = 2.182291667

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 2.182291667

Calculate the square root of the right side: 1.477258159

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.477258159 and -1.477258159.


Subproblem 1
x + -0.875 = 1.477258159

Simplifying
x + -0.875 = 1.477258159

Reorder the terms:
-0.875 + x = 1.477258159

Solving
-0.875 + x = 1.477258159

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.477258159 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.477258159 + 0.875
x = 1.477258159 + 0.875

Combine like terms: 1.477258159 + 0.875 = 2.352258159
x = 2.352258159

Simplifying
x = 2.352258159


Subproblem 2
x + -0.875 = -1.477258159

Simplifying
x + -0.875 = -1.477258159

Reorder the terms:
-0.875 + x = -1.477258159

Solving
-0.875 + x = -1.477258159

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.477258159 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.477258159 + 0.875
x = -1.477258159 + 0.875

Combine like terms: -1.477258159 + 0.875 = -0.602258159
x = -0.602258159

Simplifying
x = -0.602258159


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.352258159, -0.602258159}

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