15v^2-70v+49=0

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Solution for 15v^2-70v+49=0 equation: 


Simplifying
15v2 + -70v + 49 = 0

Reorder the terms:
49 + -70v + 15v2 = 0

Solving
49 + -70v + 15v2 = 0

Solving for variable 'v'.

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

Divide each side by '15'.
3.266666667 + -4.666666667v + v2 = 0

Move the constant term to the right:

Add '-3.266666667' to each side of the equation.
3.266666667 + -4.666666667v + -3.266666667 + v2 = 0 + -3.266666667

Reorder the terms:
3.266666667 + -3.266666667 + -4.666666667v + v2 = 0 + -3.266666667

Combine like terms: 3.266666667 + -3.266666667 = 0.000000000
0.000000000 + -4.666666667v + v2 = 0 + -3.266666667
-4.666666667v + v2 = 0 + -3.266666667

Combine like terms: 0 + -3.266666667 = -3.266666667
-4.666666667v + v2 = -3.266666667

The v term is -4.666666667v.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667v + 5.444444448 + v2 = -3.266666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667v + v2 = -3.266666667 + 5.444444448

Combine like terms: -3.266666667 + 5.444444448 = 2.177777781
5.444444448 + -4.666666667v + v2 = 2.177777781

Factor a perfect square on the left side:
(v + -2.333333334)(v + -2.333333334) = 2.177777781

Calculate the square root of the right side: 1.475729576

Break this problem into two subproblems by setting 
(v + -2.333333334) equal to 1.475729576 and -1.475729576.


Subproblem 1
v + -2.333333334 = 1.475729576

Simplifying
v + -2.333333334 = 1.475729576

Reorder the terms:
-2.333333334 + v = 1.475729576

Solving
-2.333333334 + v = 1.475729576

Solving for variable 'v'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + v = 1.475729576 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + v = 1.475729576 + 2.333333334
v = 1.475729576 + 2.333333334

Combine like terms: 1.475729576 + 2.333333334 = 3.80906291
v = 3.80906291

Simplifying
v = 3.80906291


Subproblem 2
v + -2.333333334 = -1.475729576

Simplifying
v + -2.333333334 = -1.475729576

Reorder the terms:
-2.333333334 + v = -1.475729576

Solving
-2.333333334 + v = -1.475729576

Solving for variable 'v'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + v = -1.475729576 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + v = -1.475729576 + 2.333333334
v = -1.475729576 + 2.333333334

Combine like terms: -1.475729576 + 2.333333334 = 0.857603758
v = 0.857603758

Simplifying
v = 0.857603758


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.80906291, 0.857603758}

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