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Simplifying 5v2 + 15v + -2 = 0 Reorder the terms: -2 + 15v + 5v2 = 0 Solving -2 + 15v + 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'. -0.4 + 3v + v2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 3v + 0.4 + v2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 3v + v2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 3v + v2 = 0 + 0.4 3v + v2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 3v + v2 = 0.4 The v term is 3v. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3v + 2.25 + v2 = 0.4 + 2.25 Reorder the terms: 2.25 + 3v + v2 = 0.4 + 2.25 Combine like terms: 0.4 + 2.25 = 2.65 2.25 + 3v + v2 = 2.65 Factor a perfect square on the left side: (v + 1.5)(v + 1.5) = 2.65 Calculate the square root of the right side: 1.62788206 Break this problem into two subproblems by setting (v + 1.5) equal to 1.62788206 and -1.62788206.Subproblem 1
v + 1.5 = 1.62788206 Simplifying v + 1.5 = 1.62788206 Reorder the terms: 1.5 + v = 1.62788206 Solving 1.5 + v = 1.62788206 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = 1.62788206 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = 1.62788206 + -1.5 v = 1.62788206 + -1.5 Combine like terms: 1.62788206 + -1.5 = 0.12788206 v = 0.12788206 Simplifying v = 0.12788206Subproblem 2
v + 1.5 = -1.62788206 Simplifying v + 1.5 = -1.62788206 Reorder the terms: 1.5 + v = -1.62788206 Solving 1.5 + v = -1.62788206 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + v = -1.62788206 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + v = -1.62788206 + -1.5 v = -1.62788206 + -1.5 Combine like terms: -1.62788206 + -1.5 = -3.12788206 v = -3.12788206 Simplifying v = -3.12788206Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.12788206, -3.12788206}
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