16v^2+17v-45=0

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Solution for 16v^2+17v-45=0 equation:


Simplifying
16v2 + 17v + -45 = 0

Reorder the terms:
-45 + 17v + 16v2 = 0

Solving
-45 + 17v + 16v2 = 0

Solving for variable 'v'.

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

Divide each side by '16'.
-2.8125 + 1.0625v + v2 = 0

Move the constant term to the right:

Add '2.8125' to each side of the equation.
-2.8125 + 1.0625v + 2.8125 + v2 = 0 + 2.8125

Reorder the terms:
-2.8125 + 2.8125 + 1.0625v + v2 = 0 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + 1.0625v + v2 = 0 + 2.8125
1.0625v + v2 = 0 + 2.8125

Combine like terms: 0 + 2.8125 = 2.8125
1.0625v + v2 = 2.8125

The v term is 1.0625v.  Take half its coefficient (0.53125).
Square it (0.2822265625) and add it to both sides.

Add '0.2822265625' to each side of the equation.
1.0625v + 0.2822265625 + v2 = 2.8125 + 0.2822265625

Reorder the terms:
0.2822265625 + 1.0625v + v2 = 2.8125 + 0.2822265625

Combine like terms: 2.8125 + 0.2822265625 = 3.0947265625
0.2822265625 + 1.0625v + v2 = 3.0947265625

Factor a perfect square on the left side:
(v + 0.53125)(v + 0.53125) = 3.0947265625

Calculate the square root of the right side: 1.759183493

Break this problem into two subproblems by setting 
(v + 0.53125) equal to 1.759183493 and -1.759183493.

Subproblem 1

v + 0.53125 = 1.759183493 Simplifying v + 0.53125 = 1.759183493 Reorder the terms: 0.53125 + v = 1.759183493 Solving 0.53125 + v = 1.759183493 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + v = 1.759183493 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + v = 1.759183493 + -0.53125 v = 1.759183493 + -0.53125 Combine like terms: 1.759183493 + -0.53125 = 1.227933493 v = 1.227933493 Simplifying v = 1.227933493

Subproblem 2

v + 0.53125 = -1.759183493 Simplifying v + 0.53125 = -1.759183493 Reorder the terms: 0.53125 + v = -1.759183493 Solving 0.53125 + v = -1.759183493 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + v = -1.759183493 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + v = -1.759183493 + -0.53125 v = -1.759183493 + -0.53125 Combine like terms: -1.759183493 + -0.53125 = -2.290433493 v = -2.290433493 Simplifying v = -2.290433493

Solution

The solution to the problem is based on the solutions from the subproblems. v = {1.227933493, -2.290433493}

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