-4v^2-116v=-192

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Solution for -4v^2-116v=-192 equation:


Simplifying
-4v2 + -116v = -192

Reorder the terms:
-116v + -4v2 = -192

Solving
-116v + -4v2 = -192

Solving for variable 'v'.

Reorder the terms:
192 + -116v + -4v2 = -192 + 192

Combine like terms: -192 + 192 = 0
192 + -116v + -4v2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(48 + -29v + -1v2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(48 + -29v + -1v2)' equal to zero and attempt to solve: Simplifying 48 + -29v + -1v2 = 0 Solving 48 + -29v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 29v + v2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 29v + 48 + v2 = 0 + 48 Reorder the terms: -48 + 48 + 29v + v2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 29v + v2 = 0 + 48 29v + v2 = 0 + 48 Combine like terms: 0 + 48 = 48 29v + v2 = 48 The v term is 29v. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29v + 210.25 + v2 = 48 + 210.25 Reorder the terms: 210.25 + 29v + v2 = 48 + 210.25 Combine like terms: 48 + 210.25 = 258.25 210.25 + 29v + v2 = 258.25 Factor a perfect square on the left side: (v + 14.5)(v + 14.5) = 258.25 Calculate the square root of the right side: 16.07015868 Break this problem into two subproblems by setting (v + 14.5) equal to 16.07015868 and -16.07015868.

Subproblem 1

v + 14.5 = 16.07015868 Simplifying v + 14.5 = 16.07015868 Reorder the terms: 14.5 + v = 16.07015868 Solving 14.5 + v = 16.07015868 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + v = 16.07015868 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + v = 16.07015868 + -14.5 v = 16.07015868 + -14.5 Combine like terms: 16.07015868 + -14.5 = 1.57015868 v = 1.57015868 Simplifying v = 1.57015868

Subproblem 2

v + 14.5 = -16.07015868 Simplifying v + 14.5 = -16.07015868 Reorder the terms: 14.5 + v = -16.07015868 Solving 14.5 + v = -16.07015868 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + v = -16.07015868 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + v = -16.07015868 + -14.5 v = -16.07015868 + -14.5 Combine like terms: -16.07015868 + -14.5 = -30.57015868 v = -30.57015868 Simplifying v = -30.57015868

Solution

The solution to the problem is based on the solutions from the subproblems. v = {1.57015868, -30.57015868}

Solution

v = {1.57015868, -30.57015868}

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