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Simplifying v2 + 14v + -72 = 6 Reorder the terms: -72 + 14v + v2 = 6 Solving -72 + 14v + v2 = 6 Solving for variable 'v'. Reorder the terms: -72 + -6 + 14v + v2 = 6 + -6 Combine like terms: -72 + -6 = -78 -78 + 14v + v2 = 6 + -6 Combine like terms: 6 + -6 = 0 -78 + 14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 14v + 78 + v2 = 0 + 78 Reorder the terms: -78 + 78 + 14v + v2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 14v + v2 = 0 + 78 14v + v2 = 0 + 78 Combine like terms: 0 + 78 = 78 14v + v2 = 78 The v term is 14v. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14v + 49 + v2 = 78 + 49 Reorder the terms: 49 + 14v + v2 = 78 + 49 Combine like terms: 78 + 49 = 127 49 + 14v + v2 = 127 Factor a perfect square on the left side: (v + 7)(v + 7) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (v + 7) equal to 11.26942767 and -11.26942767.Subproblem 1
v + 7 = 11.26942767 Simplifying v + 7 = 11.26942767 Reorder the terms: 7 + v = 11.26942767 Solving 7 + v = 11.26942767 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 11.26942767 + -7 Combine like terms: 7 + -7 = 0 0 + v = 11.26942767 + -7 v = 11.26942767 + -7 Combine like terms: 11.26942767 + -7 = 4.26942767 v = 4.26942767 Simplifying v = 4.26942767Subproblem 2
v + 7 = -11.26942767 Simplifying v + 7 = -11.26942767 Reorder the terms: 7 + v = -11.26942767 Solving 7 + v = -11.26942767 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = -11.26942767 + -7 Combine like terms: 7 + -7 = 0 0 + v = -11.26942767 + -7 v = -11.26942767 + -7 Combine like terms: -11.26942767 + -7 = -18.26942767 v = -18.26942767 Simplifying v = -18.26942767Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.26942767, -18.26942767}
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