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Simplifying 8v2 + -40v + -36 = 0 Reorder the terms: -36 + -40v + 8v2 = 0 Solving -36 + -40v + 8v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -10v + 2v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -10v + 2v2)' equal to zero and attempt to solve: Simplifying -9 + -10v + 2v2 = 0 Solving -9 + -10v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -5v + v2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -5v + 4.5 + v2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -5v + v2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -5v + v2 = 0 + 4.5 -5v + v2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -5v + v2 = 4.5 The v term is -5v. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5v + 6.25 + v2 = 4.5 + 6.25 Reorder the terms: 6.25 + -5v + v2 = 4.5 + 6.25 Combine like terms: 4.5 + 6.25 = 10.75 6.25 + -5v + v2 = 10.75 Factor a perfect square on the left side: (v + -2.5)(v + -2.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (v + -2.5) equal to 3.278719262 and -3.278719262.Subproblem 1
v + -2.5 = 3.278719262 Simplifying v + -2.5 = 3.278719262 Reorder the terms: -2.5 + v = 3.278719262 Solving -2.5 + v = 3.278719262 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = 3.278719262 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = 3.278719262 + 2.5 v = 3.278719262 + 2.5 Combine like terms: 3.278719262 + 2.5 = 5.778719262 v = 5.778719262 Simplifying v = 5.778719262Subproblem 2
v + -2.5 = -3.278719262 Simplifying v + -2.5 = -3.278719262 Reorder the terms: -2.5 + v = -3.278719262 Solving -2.5 + v = -3.278719262 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + v = -3.278719262 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + v = -3.278719262 + 2.5 v = -3.278719262 + 2.5 Combine like terms: -3.278719262 + 2.5 = -0.778719262 v = -0.778719262 Simplifying v = -0.778719262Solution
The solution to the problem is based on the solutions from the subproblems. v = {5.778719262, -0.778719262}Solution
v = {5.778719262, -0.778719262}
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