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Simplifying 0 = -16v4 + 48v3 + 492v2 Reorder the terms: 0 = 492v2 + 48v3 + -16v4 Solving 0 = 492v2 + 48v3 + -16v4 Solving for variable 'v'. Remove the zero: -492v2 + -48v3 + 16v4 = 492v2 + 48v3 + -16v4 + -492v2 + -48v3 + 16v4 Reorder the terms: -492v2 + -48v3 + 16v4 = 492v2 + -492v2 + 48v3 + -48v3 + -16v4 + 16v4 Combine like terms: 492v2 + -492v2 = 0 -492v2 + -48v3 + 16v4 = 0 + 48v3 + -48v3 + -16v4 + 16v4 -492v2 + -48v3 + 16v4 = 48v3 + -48v3 + -16v4 + 16v4 Combine like terms: 48v3 + -48v3 = 0 -492v2 + -48v3 + 16v4 = 0 + -16v4 + 16v4 -492v2 + -48v3 + 16v4 = -16v4 + 16v4 Combine like terms: -16v4 + 16v4 = 0 -492v2 + -48v3 + 16v4 = 0 Factor out the Greatest Common Factor (GCF), '4v2'. 4v2(-123 + -12v + 4v2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve: Simplifying v2 = 0 Solving v2 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v2 = 0 Take the square root of each side: v = {0}Subproblem 2
Set the factor '(-123 + -12v + 4v2)' equal to zero and attempt to solve: Simplifying -123 + -12v + 4v2 = 0 Solving -123 + -12v + 4v2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -30.75 + -3v + v2 = 0 Move the constant term to the right: Add '30.75' to each side of the equation. -30.75 + -3v + 30.75 + v2 = 0 + 30.75 Reorder the terms: -30.75 + 30.75 + -3v + v2 = 0 + 30.75 Combine like terms: -30.75 + 30.75 = 0.00 0.00 + -3v + v2 = 0 + 30.75 -3v + v2 = 0 + 30.75 Combine like terms: 0 + 30.75 = 30.75 -3v + v2 = 30.75 The v term is -3v. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3v + 2.25 + v2 = 30.75 + 2.25 Reorder the terms: 2.25 + -3v + v2 = 30.75 + 2.25 Combine like terms: 30.75 + 2.25 = 33 2.25 + -3v + v2 = 33 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (v + -1.5) equal to 5.744562647 and -5.744562647.Subproblem 1
v + -1.5 = 5.744562647 Simplifying v + -1.5 = 5.744562647 Reorder the terms: -1.5 + v = 5.744562647 Solving -1.5 + v = 5.744562647 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = 5.744562647 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = 5.744562647 + 1.5 v = 5.744562647 + 1.5 Combine like terms: 5.744562647 + 1.5 = 7.244562647 v = 7.244562647 Simplifying v = 7.244562647Subproblem 2
v + -1.5 = -5.744562647 Simplifying v + -1.5 = -5.744562647 Reorder the terms: -1.5 + v = -5.744562647 Solving -1.5 + v = -5.744562647 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + v = -5.744562647 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = -5.744562647 + 1.5 v = -5.744562647 + 1.5 Combine like terms: -5.744562647 + 1.5 = -4.244562647 v = -4.244562647 Simplifying v = -4.244562647Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.244562647, -4.244562647}Solution
v = {0, 7.244562647, -4.244562647}
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