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Simplifying 10v2 + 25v + -30 = 0 Reorder the terms: -30 + 25v + 10v2 = 0 Solving -30 + 25v + 10v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 5v + 2v2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + 5v + 2v2)' equal to zero and attempt to solve: Simplifying -6 + 5v + 2v2 = 0 Solving -6 + 5v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 2.5v + v2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.5v + 3 + v2 = 0 + 3 Reorder the terms: -3 + 3 + 2.5v + v2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.5v + v2 = 0 + 3 2.5v + v2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.5v + v2 = 3 The v term is 2.5v. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5v + 1.5625 + v2 = 3 + 1.5625 Reorder the terms: 1.5625 + 2.5v + v2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + 2.5v + v2 = 4.5625 Factor a perfect square on the left side: (v + 1.25)(v + 1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (v + 1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
v + 1.25 = 2.136000936 Simplifying v + 1.25 = 2.136000936 Reorder the terms: 1.25 + v = 2.136000936 Solving 1.25 + v = 2.136000936 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + v = 2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + v = 2.136000936 + -1.25 v = 2.136000936 + -1.25 Combine like terms: 2.136000936 + -1.25 = 0.886000936 v = 0.886000936 Simplifying v = 0.886000936Subproblem 2
v + 1.25 = -2.136000936 Simplifying v + 1.25 = -2.136000936 Reorder the terms: 1.25 + v = -2.136000936 Solving 1.25 + v = -2.136000936 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + v = -2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + v = -2.136000936 + -1.25 v = -2.136000936 + -1.25 Combine like terms: -2.136000936 + -1.25 = -3.386000936 v = -3.386000936 Simplifying v = -3.386000936Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.886000936, -3.386000936}Solution
v = {0.886000936, -3.386000936}
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