4.9x^2-14x-10=0

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Solution for 4.9x^2-14x-10=0 equation: 


Simplifying
4.9x2 + -14x + -10 = 0

Reorder the terms:
-10 + -14x + 4.9x2 = 0

Solving
-10 + -14x + 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'.
-2.040816327 + -2.857142857x + x2 = 0

Move the constant term to the right:

Add '2.040816327' to each side of the equation.
-2.040816327 + -2.857142857x + 2.040816327 + x2 = 0 + 2.040816327

Reorder the terms:
-2.040816327 + 2.040816327 + -2.857142857x + x2 = 0 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + -2.857142857x + x2 = 0 + 2.040816327
-2.857142857x + x2 = 0 + 2.040816327

Combine like terms: 0 + 2.040816327 = 2.040816327
-2.857142857x + x2 = 2.040816327

The x term is -2.857142857x.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857x + 2.040816328 + x2 = 2.040816327 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857x + x2 = 2.040816327 + 2.040816328

Combine like terms: 2.040816327 + 2.040816328 = 4.081632655
2.040816328 + -2.857142857x + x2 = 4.081632655

Factor a perfect square on the left side:
(x + -1.428571429)(x + -1.428571429) = 4.081632655

Calculate the square root of the right side: 2.02030509

Break this problem into two subproblems by setting 
(x + -1.428571429) equal to 2.02030509 and -2.02030509.


Subproblem 1
x + -1.428571429 = 2.02030509

Simplifying
x + -1.428571429 = 2.02030509

Reorder the terms:
-1.428571429 + x = 2.02030509

Solving
-1.428571429 + x = 2.02030509

Solving for variable 'x'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + x = 2.02030509 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + x = 2.02030509 + 1.428571429
x = 2.02030509 + 1.428571429

Combine like terms: 2.02030509 + 1.428571429 = 3.448876519
x = 3.448876519

Simplifying
x = 3.448876519


Subproblem 2
x + -1.428571429 = -2.02030509

Simplifying
x + -1.428571429 = -2.02030509

Reorder the terms:
-1.428571429 + x = -2.02030509

Solving
-1.428571429 + x = -2.02030509

Solving for variable 'x'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + x = -2.02030509 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + x = -2.02030509 + 1.428571429
x = -2.02030509 + 1.428571429

Combine like terms: -2.02030509 + 1.428571429 = -0.591733661
x = -0.591733661

Simplifying
x = -0.591733661


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.448876519, -0.591733661}

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