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Simplifying 10v2 + 6v = 3 Reorder the terms: 6v + 10v2 = 3 Solving 6v + 10v2 = 3 Solving for variable 'v'. Reorder the terms: -3 + 6v + 10v2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 6v + 10v2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.6v + v2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.6v + 0.3 + v2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.6v + v2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.6v + v2 = 0 + 0.3 0.6v + v2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.6v + v2 = 0.3 The v term is 0.6v. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6v + 0.09 + v2 = 0.3 + 0.09 Reorder the terms: 0.09 + 0.6v + v2 = 0.3 + 0.09 Combine like terms: 0.3 + 0.09 = 0.39 0.09 + 0.6v + v2 = 0.39 Factor a perfect square on the left side: (v + 0.3)(v + 0.3) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (v + 0.3) equal to 0.6244998 and -0.6244998.Subproblem 1
v + 0.3 = 0.6244998 Simplifying v + 0.3 = 0.6244998 Reorder the terms: 0.3 + v = 0.6244998 Solving 0.3 + v = 0.6244998 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + v = 0.6244998 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + v = 0.6244998 + -0.3 v = 0.6244998 + -0.3 Combine like terms: 0.6244998 + -0.3 = 0.3244998 v = 0.3244998 Simplifying v = 0.3244998Subproblem 2
v + 0.3 = -0.6244998 Simplifying v + 0.3 = -0.6244998 Reorder the terms: 0.3 + v = -0.6244998 Solving 0.3 + v = -0.6244998 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + v = -0.6244998 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + v = -0.6244998 + -0.3 v = -0.6244998 + -0.3 Combine like terms: -0.6244998 + -0.3 = -0.9244998 v = -0.9244998 Simplifying v = -0.9244998Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.3244998, -0.9244998}
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