4.9x^2-10x+5.1=0

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Solution for 4.9x^2-10x+5.1=0 equation: 


Simplifying
4.9x2 + -10x + 5.1 = 0

Reorder the terms:
5.1 + -10x + 4.9x2 = 0

Solving
5.1 + -10x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
1.040816327 + -2.040816327x + x2 = 0

Move the constant term to the right:

Add '-1.040816327' to each side of the equation.
1.040816327 + -2.040816327x + -1.040816327 + x2 = 0 + -1.040816327

Reorder the terms:
1.040816327 + -1.040816327 + -2.040816327x + x2 = 0 + -1.040816327

Combine like terms: 1.040816327 + -1.040816327 = 0.000000000
0.000000000 + -2.040816327x + x2 = 0 + -1.040816327
-2.040816327x + x2 = 0 + -1.040816327

Combine like terms: 0 + -1.040816327 = -1.040816327
-2.040816327x + x2 = -1.040816327

The x term is -2.040816327x.  Take half its coefficient (-1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
-2.040816327x + 1.041232821 + x2 = -1.040816327 + 1.041232821

Reorder the terms:
1.041232821 + -2.040816327x + x2 = -1.040816327 + 1.041232821

Combine like terms: -1.040816327 + 1.041232821 = 0.000416494
1.041232821 + -2.040816327x + x2 = 0.000416494

Factor a perfect square on the left side:
(x + -1.020408164)(x + -1.020408164) = 0.000416494

Calculate the square root of the right side: 0.020408185

Break this problem into two subproblems by setting 
(x + -1.020408164) equal to 0.020408185 and -0.020408185.


Subproblem 1
x + -1.020408164 = 0.020408185

Simplifying
x + -1.020408164 = 0.020408185

Reorder the terms:
-1.020408164 + x = 0.020408185

Solving
-1.020408164 + x = 0.020408185

Solving for variable 'x'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + x = 0.020408185 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + x = 0.020408185 + 1.020408164
x = 0.020408185 + 1.020408164

Combine like terms: 0.020408185 + 1.020408164 = 1.040816349
x = 1.040816349

Simplifying
x = 1.040816349


Subproblem 2
x + -1.020408164 = -0.020408185

Simplifying
x + -1.020408164 = -0.020408185

Reorder the terms:
-1.020408164 + x = -0.020408185

Solving
-1.020408164 + x = -0.020408185

Solving for variable 'x'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + x = -0.020408185 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + x = -0.020408185 + 1.020408164
x = -0.020408185 + 1.020408164

Combine like terms: -0.020408185 + 1.020408164 = 0.999999979
x = 0.999999979

Simplifying
x = 0.999999979


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.040816349, 0.999999979}

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