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Simplifying 5v2 + 12v + -6 = 0 Reorder the terms: -6 + 12v + 5v2 = 0 Solving -6 + 12v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 2.4v + v2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 2.4v + 1.2 + v2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 2.4v + v2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 2.4v + v2 = 0 + 1.2 2.4v + v2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 2.4v + v2 = 1.2 The v term is 2.4v. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4v + 1.44 + v2 = 1.2 + 1.44 Reorder the terms: 1.44 + 2.4v + v2 = 1.2 + 1.44 Combine like terms: 1.2 + 1.44 = 2.64 1.44 + 2.4v + v2 = 2.64 Factor a perfect square on the left side: (v + 1.2)(v + 1.2) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (v + 1.2) equal to 1.624807681 and -1.624807681.Subproblem 1
v + 1.2 = 1.624807681 Simplifying v + 1.2 = 1.624807681 Reorder the terms: 1.2 + v = 1.624807681 Solving 1.2 + v = 1.624807681 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + v = 1.624807681 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + v = 1.624807681 + -1.2 v = 1.624807681 + -1.2 Combine like terms: 1.624807681 + -1.2 = 0.424807681 v = 0.424807681 Simplifying v = 0.424807681Subproblem 2
v + 1.2 = -1.624807681 Simplifying v + 1.2 = -1.624807681 Reorder the terms: 1.2 + v = -1.624807681 Solving 1.2 + v = -1.624807681 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + v = -1.624807681 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + v = -1.624807681 + -1.2 v = -1.624807681 + -1.2 Combine like terms: -1.624807681 + -1.2 = -2.824807681 v = -2.824807681 Simplifying v = -2.824807681Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.424807681, -2.824807681}
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