49v^2-49v+9=0

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Solution for 49v^2-49v+9=0 equation:


Simplifying
49v2 + -49v + 9 = 0

Reorder the terms:
9 + -49v + 49v2 = 0

Solving
9 + -49v + 49v2 = 0

Solving for variable 'v'.

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

Divide each side by '49'.
0.1836734694 + -1v + v2 = 0

Move the constant term to the right:

Add '-0.1836734694' to each side of the equation.
0.1836734694 + -1v + -0.1836734694 + v2 = 0 + -0.1836734694

Reorder the terms:
0.1836734694 + -0.1836734694 + -1v + v2 = 0 + -0.1836734694

Combine like terms: 0.1836734694 + -0.1836734694 = 0.0000000000
0.0000000000 + -1v + v2 = 0 + -0.1836734694
-1v + v2 = 0 + -0.1836734694

Combine like terms: 0 + -0.1836734694 = -0.1836734694
-1v + v2 = -0.1836734694

The v term is -1v.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1v + 0.25 + v2 = -0.1836734694 + 0.25

Reorder the terms:
0.25 + -1v + v2 = -0.1836734694 + 0.25

Combine like terms: -0.1836734694 + 0.25 = 0.0663265306
0.25 + -1v + v2 = 0.0663265306

Factor a perfect square on the left side:
(v + -0.5)(v + -0.5) = 0.0663265306

Calculate the square root of the right side: 0.257539377

Break this problem into two subproblems by setting 
(v + -0.5) equal to 0.257539377 and -0.257539377.

Subproblem 1

v + -0.5 = 0.257539377 Simplifying v + -0.5 = 0.257539377 Reorder the terms: -0.5 + v = 0.257539377 Solving -0.5 + v = 0.257539377 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 0.257539377 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 0.257539377 + 0.5 v = 0.257539377 + 0.5 Combine like terms: 0.257539377 + 0.5 = 0.757539377 v = 0.757539377 Simplifying v = 0.757539377

Subproblem 2

v + -0.5 = -0.257539377 Simplifying v + -0.5 = -0.257539377 Reorder the terms: -0.5 + v = -0.257539377 Solving -0.5 + v = -0.257539377 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -0.257539377 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -0.257539377 + 0.5 v = -0.257539377 + 0.5 Combine like terms: -0.257539377 + 0.5 = 0.242460623 v = 0.242460623 Simplifying v = 0.242460623

Solution

The solution to the problem is based on the solutions from the subproblems. v = {0.757539377, 0.242460623}

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