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Simplifying -10v2 + -4v + 3 = 0 Reorder the terms: 3 + -4v + -10v2 = 0 Solving 3 + -4v + -10v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + 0.4v + v2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.4v + 0.3 + v2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.4v + v2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.4v + v2 = 0 + 0.3 0.4v + v2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 0.4v + v2 = 0.3 The v term is 0.4v. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4v + 0.04 + v2 = 0.3 + 0.04 Reorder the terms: 0.04 + 0.4v + v2 = 0.3 + 0.04 Combine like terms: 0.3 + 0.04 = 0.34 0.04 + 0.4v + v2 = 0.34 Factor a perfect square on the left side: (v + 0.2)(v + 0.2) = 0.34 Calculate the square root of the right side: 0.583095189 Break this problem into two subproblems by setting (v + 0.2) equal to 0.583095189 and -0.583095189.Subproblem 1
v + 0.2 = 0.583095189 Simplifying v + 0.2 = 0.583095189 Reorder the terms: 0.2 + v = 0.583095189 Solving 0.2 + v = 0.583095189 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + v = 0.583095189 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + v = 0.583095189 + -0.2 v = 0.583095189 + -0.2 Combine like terms: 0.583095189 + -0.2 = 0.383095189 v = 0.383095189 Simplifying v = 0.383095189Subproblem 2
v + 0.2 = -0.583095189 Simplifying v + 0.2 = -0.583095189 Reorder the terms: 0.2 + v = -0.583095189 Solving 0.2 + v = -0.583095189 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + v = -0.583095189 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + v = -0.583095189 + -0.2 v = -0.583095189 + -0.2 Combine like terms: -0.583095189 + -0.2 = -0.783095189 v = -0.783095189 Simplifying v = -0.783095189Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.383095189, -0.783095189}
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