1.2(x^2+1)=2.5x

Solution for 1.2(x^2+1)=2.5x equation:

Simplifying
1.2(x2 + 1) = 2.5x

Reorder the terms:
1.2(1 + x2) = 2.5x
(1 * 1.2 + x2 * 1.2) = 2.5x
(1.2 + 1.2x2) = 2.5x

Solving
1.2 + 1.2x2 = 2.5x

Solving for variable 'x'.

Reorder the terms:
1.2 + -2.5x + 1.2x2 = 2.5x + -2.5x

Combine like terms: 2.5x + -2.5x = 0.0
1.2 + -2.5x + 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 + -2.083333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.083333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.083333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.083333333x + x2 = 0 + -1
-2.083333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.083333333x + x2 = -1

The x term is -2.083333333x.  Take half its coefficient (-1.041666667).
Square it (1.085069445) and add it to both sides.

Add '1.085069445' to each side of the equation.
-2.083333333x + 1.085069445 + x2 = -1 + 1.085069445

Reorder the terms:
1.085069445 + -2.083333333x + x2 = -1 + 1.085069445

Combine like terms: -1 + 1.085069445 = 0.085069445
1.085069445 + -2.083333333x + x2 = 0.085069445

Factor a perfect square on the left side:
(x + -1.041666667)(x + -1.041666667) = 0.085069445

Calculate the square root of the right side: 0.291666668

Break this problem into two subproblems by setting 
(x + -1.041666667) equal to 0.291666668 and -0.291666668.

Subproblem 1
x + -1.041666667 = 0.291666668

Simplifying
x + -1.041666667 = 0.291666668

Reorder the terms:
-1.041666667 + x = 0.291666668

Solving
-1.041666667 + x = 0.291666668

Solving for variable 'x'.

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

Add '1.041666667' to each side of the equation.
-1.041666667 + 1.041666667 + x = 0.291666668 + 1.041666667

Combine like terms: -1.041666667 + 1.041666667 = 0.000000000
0.000000000 + x = 0.291666668 + 1.041666667
x = 0.291666668 + 1.041666667

Combine like terms: 0.291666668 + 1.041666667 = 1.333333335
x = 1.333333335

Simplifying
x = 1.333333335

Subproblem 2
x + -1.041666667 = -0.291666668

Simplifying
x + -1.041666667 = -0.291666668

Reorder the terms:
-1.041666667 + x = -0.291666668

Solving
-1.041666667 + x = -0.291666668

Solving for variable 'x'.

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

Add '1.041666667' to each side of the equation.
-1.041666667 + 1.041666667 + x = -0.291666668 + 1.041666667

Combine like terms: -1.041666667 + 1.041666667 = 0.000000000
0.000000000 + x = -0.291666668 + 1.041666667
x = -0.291666668 + 1.041666667

Combine like terms: -0.291666668 + 1.041666667 = 0.749999999
x = 0.749999999

Simplifying
x = 0.749999999

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.333333335, 0.749999999}