x^2-4.8x+2.9=0

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Solution for x^2-4.8x+2.9=0 equation: 


Simplifying
x2 + -4.8x + 2.9 = 0

Reorder the terms:
2.9 + -4.8x + x2 = 0

Solving
2.9 + -4.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.9' to each side of the equation.
2.9 + -4.8x + -2.9 + x2 = 0 + -2.9

Reorder the terms:
2.9 + -2.9 + -4.8x + x2 = 0 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + -4.8x + x2 = 0 + -2.9
-4.8x + x2 = 0 + -2.9

Combine like terms: 0 + -2.9 = -2.9
-4.8x + x2 = -2.9

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = -2.9 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = -2.9 + 5.76

Combine like terms: -2.9 + 5.76 = 2.86
5.76 + -4.8x + x2 = 2.86

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 2.86

Calculate the square root of the right side: 1.691153453

Break this problem into two subproblems by setting 
(x + -2.4) equal to 1.691153453 and -1.691153453.


Subproblem 1
x + -2.4 = 1.691153453

Simplifying
x + -2.4 = 1.691153453

Reorder the terms:
-2.4 + x = 1.691153453

Solving
-2.4 + x = 1.691153453

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = 1.691153453 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 1.691153453 + 2.4
x = 1.691153453 + 2.4

Combine like terms: 1.691153453 + 2.4 = 4.091153453
x = 4.091153453

Simplifying
x = 4.091153453


Subproblem 2
x + -2.4 = -1.691153453

Simplifying
x + -2.4 = -1.691153453

Reorder the terms:
-2.4 + x = -1.691153453

Solving
-2.4 + x = -1.691153453

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = -1.691153453 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -1.691153453 + 2.4
x = -1.691153453 + 2.4

Combine like terms: -1.691153453 + 2.4 = 0.708846547
x = 0.708846547

Simplifying
x = 0.708846547


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.091153453, 0.708846547}

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