x^2-4.8*0.01+4.8x=0

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Solution for x^2-4.8*0.01+4.8x=0 equation: 


Simplifying
x2 + -4.8 * 0.01 + 4.8x = 0

Multiply -4.8 * 0.01
x2 + -0.048 + 4.8x = 0

Reorder the terms:
-0.048 + 4.8x + x2 = 0

Solving
-0.048 + 4.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.048' to each side of the equation.
-0.048 + 4.8x + 0.048 + x2 = 0 + 0.048

Reorder the terms:
-0.048 + 0.048 + 4.8x + x2 = 0 + 0.048

Combine like terms: -0.048 + 0.048 = 0.000
0.000 + 4.8x + x2 = 0 + 0.048
4.8x + x2 = 0 + 0.048

Combine like terms: 0 + 0.048 = 0.048
4.8x + x2 = 0.048

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 = 0.048 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = 0.048 + 5.76

Combine like terms: 0.048 + 5.76 = 5.808
5.76 + 4.8x + x2 = 5.808

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 5.808

Calculate the square root of the right side: 2.409979253

Break this problem into two subproblems by setting 
(x + 2.4) equal to 2.409979253 and -2.409979253.


Subproblem 1
x + 2.4 = 2.409979253

Simplifying
x + 2.4 = 2.409979253

Reorder the terms:
2.4 + x = 2.409979253

Solving
2.4 + x = 2.409979253

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 = 2.409979253 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 2.409979253 + -2.4
x = 2.409979253 + -2.4

Combine like terms: 2.409979253 + -2.4 = 0.009979253
x = 0.009979253

Simplifying
x = 0.009979253


Subproblem 2
x + 2.4 = -2.409979253

Simplifying
x + 2.4 = -2.409979253

Reorder the terms:
2.4 + x = -2.409979253

Solving
2.4 + x = -2.409979253

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 = -2.409979253 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -2.409979253 + -2.4
x = -2.409979253 + -2.4

Combine like terms: -2.409979253 + -2.4 = -4.809979253
x = -4.809979253

Simplifying
x = -4.809979253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.009979253, -4.809979253}

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