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Simplifying 3v2 + -9v = 5 Reorder the terms: -9v + 3v2 = 5 Solving -9v + 3v2 = 5 Solving for variable 'v'. Reorder the terms: -5 + -9v + 3v2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -9v + 3v2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + -3v + v2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -3v + 1.666666667 + v2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -3v + v2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -3v + v2 = 0 + 1.666666667 -3v + v2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -3v + v2 = 1.666666667 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 = 1.666666667 + 2.25 Reorder the terms: 2.25 + -3v + v2 = 1.666666667 + 2.25 Combine like terms: 1.666666667 + 2.25 = 3.916666667 2.25 + -3v + v2 = 3.916666667 Factor a perfect square on the left side: (v + -1.5)(v + -1.5) = 3.916666667 Calculate the square root of the right side: 1.979057015 Break this problem into two subproblems by setting (v + -1.5) equal to 1.979057015 and -1.979057015.Subproblem 1
v + -1.5 = 1.979057015 Simplifying v + -1.5 = 1.979057015 Reorder the terms: -1.5 + v = 1.979057015 Solving -1.5 + v = 1.979057015 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 = 1.979057015 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = 1.979057015 + 1.5 v = 1.979057015 + 1.5 Combine like terms: 1.979057015 + 1.5 = 3.479057015 v = 3.479057015 Simplifying v = 3.479057015Subproblem 2
v + -1.5 = -1.979057015 Simplifying v + -1.5 = -1.979057015 Reorder the terms: -1.5 + v = -1.979057015 Solving -1.5 + v = -1.979057015 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 = -1.979057015 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + v = -1.979057015 + 1.5 v = -1.979057015 + 1.5 Combine like terms: -1.979057015 + 1.5 = -0.479057015 v = -0.479057015 Simplifying v = -0.479057015Solution
The solution to the problem is based on the solutions from the subproblems. v = {3.479057015, -0.479057015}
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