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Simplifying 4v2 + -44v + 84 = 0 Reorder the terms: 84 + -44v + 4v2 = 0 Solving 84 + -44v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(21 + -11v + v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(21 + -11v + v2)' equal to zero and attempt to solve: Simplifying 21 + -11v + v2 = 0 Solving 21 + -11v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -11v + -21 + v2 = 0 + -21 Reorder the terms: 21 + -21 + -11v + v2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -11v + v2 = 0 + -21 -11v + v2 = 0 + -21 Combine like terms: 0 + -21 = -21 -11v + v2 = -21 The v term is -11v. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11v + 30.25 + v2 = -21 + 30.25 Reorder the terms: 30.25 + -11v + v2 = -21 + 30.25 Combine like terms: -21 + 30.25 = 9.25 30.25 + -11v + v2 = 9.25 Factor a perfect square on the left side: (v + -5.5)(v + -5.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (v + -5.5) equal to 3.041381265 and -3.041381265.Subproblem 1
v + -5.5 = 3.041381265 Simplifying v + -5.5 = 3.041381265 Reorder the terms: -5.5 + v = 3.041381265 Solving -5.5 + v = 3.041381265 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = 3.041381265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = 3.041381265 + 5.5 v = 3.041381265 + 5.5 Combine like terms: 3.041381265 + 5.5 = 8.541381265 v = 8.541381265 Simplifying v = 8.541381265Subproblem 2
v + -5.5 = -3.041381265 Simplifying v + -5.5 = -3.041381265 Reorder the terms: -5.5 + v = -3.041381265 Solving -5.5 + v = -3.041381265 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + v = -3.041381265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + v = -3.041381265 + 5.5 v = -3.041381265 + 5.5 Combine like terms: -3.041381265 + 5.5 = 2.458618735 v = 2.458618735 Simplifying v = 2.458618735Solution
The solution to the problem is based on the solutions from the subproblems. v = {8.541381265, 2.458618735}Solution
v = {8.541381265, 2.458618735}
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