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Simplifying 10v2 + 29v + -12 = 0 Reorder the terms: -12 + 29v + 10v2 = 0 Solving -12 + 29v + 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'. -1.2 + 2.9v + v2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 2.9v + 1.2 + v2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 2.9v + v2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 2.9v + v2 = 0 + 1.2 2.9v + v2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 2.9v + v2 = 1.2 The v term is 2.9v. Take half its coefficient (1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. 2.9v + 2.1025 + v2 = 1.2 + 2.1025 Reorder the terms: 2.1025 + 2.9v + v2 = 1.2 + 2.1025 Combine like terms: 1.2 + 2.1025 = 3.3025 2.1025 + 2.9v + v2 = 3.3025 Factor a perfect square on the left side: (v + 1.45)(v + 1.45) = 3.3025 Calculate the square root of the right side: 1.817278185 Break this problem into two subproblems by setting (v + 1.45) equal to 1.817278185 and -1.817278185.Subproblem 1
v + 1.45 = 1.817278185 Simplifying v + 1.45 = 1.817278185 Reorder the terms: 1.45 + v = 1.817278185 Solving 1.45 + v = 1.817278185 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + v = 1.817278185 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + v = 1.817278185 + -1.45 v = 1.817278185 + -1.45 Combine like terms: 1.817278185 + -1.45 = 0.367278185 v = 0.367278185 Simplifying v = 0.367278185Subproblem 2
v + 1.45 = -1.817278185 Simplifying v + 1.45 = -1.817278185 Reorder the terms: 1.45 + v = -1.817278185 Solving 1.45 + v = -1.817278185 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.45' to each side of the equation. 1.45 + -1.45 + v = -1.817278185 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + v = -1.817278185 + -1.45 v = -1.817278185 + -1.45 Combine like terms: -1.817278185 + -1.45 = -3.267278185 v = -3.267278185 Simplifying v = -3.267278185Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.367278185, -3.267278185}
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