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Simplifying 6v + 79 + -1v2 = 16 Reorder the terms: 79 + 6v + -1v2 = 16 Solving 79 + 6v + -1v2 = 16 Solving for variable 'v'. Reorder the terms: 79 + -16 + 6v + -1v2 = 16 + -16 Combine like terms: 79 + -16 = 63 63 + 6v + -1v2 = 16 + -16 Combine like terms: 16 + -16 = 0 63 + 6v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + -6v + v2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + -6v + 63 + v2 = 0 + 63 Reorder the terms: -63 + 63 + -6v + v2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -6v + v2 = 0 + 63 -6v + v2 = 0 + 63 Combine like terms: 0 + 63 = 63 -6v + v2 = 63 The v term is -6v. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6v + 9 + v2 = 63 + 9 Reorder the terms: 9 + -6v + v2 = 63 + 9 Combine like terms: 63 + 9 = 72 9 + -6v + v2 = 72 Factor a perfect square on the left side: (v + -3)(v + -3) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (v + -3) equal to 8.485281374 and -8.485281374.Subproblem 1
v + -3 = 8.485281374 Simplifying v + -3 = 8.485281374 Reorder the terms: -3 + v = 8.485281374 Solving -3 + v = 8.485281374 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = 8.485281374 + 3 Combine like terms: -3 + 3 = 0 0 + v = 8.485281374 + 3 v = 8.485281374 + 3 Combine like terms: 8.485281374 + 3 = 11.485281374 v = 11.485281374 Simplifying v = 11.485281374Subproblem 2
v + -3 = -8.485281374 Simplifying v + -3 = -8.485281374 Reorder the terms: -3 + v = -8.485281374 Solving -3 + v = -8.485281374 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + v = -8.485281374 + 3 Combine like terms: -3 + 3 = 0 0 + v = -8.485281374 + 3 v = -8.485281374 + 3 Combine like terms: -8.485281374 + 3 = -5.485281374 v = -5.485281374 Simplifying v = -5.485281374Solution
The solution to the problem is based on the solutions from the subproblems. v = {11.485281374, -5.485281374}
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