-8v^2+18v+7=0

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Solution for -8v^2+18v+7=0 equation:


Simplifying
-8v2 + 18v + 7 = 0

Reorder the terms:
7 + 18v + -8v2 = 0

Solving
7 + 18v + -8v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.875 + -2.25v + v2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -2.25v + 0.875 + v2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -2.25v + v2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -2.25v + v2 = 0 + 0.875
-2.25v + v2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-2.25v + v2 = 0.875

The v term is -2.25v.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25v + 1.265625 + v2 = 0.875 + 1.265625

Reorder the terms:
1.265625 + -2.25v + v2 = 0.875 + 1.265625

Combine like terms: 0.875 + 1.265625 = 2.140625
1.265625 + -2.25v + v2 = 2.140625

Factor a perfect square on the left side:
(v + -1.125)(v + -1.125) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(v + -1.125) equal to 1.463087489 and -1.463087489.

Subproblem 1

v + -1.125 = 1.463087489 Simplifying v + -1.125 = 1.463087489 Reorder the terms: -1.125 + v = 1.463087489 Solving -1.125 + v = 1.463087489 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + v = 1.463087489 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + v = 1.463087489 + 1.125 v = 1.463087489 + 1.125 Combine like terms: 1.463087489 + 1.125 = 2.588087489 v = 2.588087489 Simplifying v = 2.588087489

Subproblem 2

v + -1.125 = -1.463087489 Simplifying v + -1.125 = -1.463087489 Reorder the terms: -1.125 + v = -1.463087489 Solving -1.125 + v = -1.463087489 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + v = -1.463087489 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + v = -1.463087489 + 1.125 v = -1.463087489 + 1.125 Combine like terms: -1.463087489 + 1.125 = -0.338087489 v = -0.338087489 Simplifying v = -0.338087489

Solution

The solution to the problem is based on the solutions from the subproblems. v = {2.588087489, -0.338087489}

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