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Simplifying v2 + 14v + -84 = 10 Reorder the terms: -84 + 14v + v2 = 10 Solving -84 + 14v + v2 = 10 Solving for variable 'v'. Reorder the terms: -84 + -10 + 14v + v2 = 10 + -10 Combine like terms: -84 + -10 = -94 -94 + 14v + v2 = 10 + -10 Combine like terms: 10 + -10 = 0 -94 + 14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 14v + 94 + v2 = 0 + 94 Reorder the terms: -94 + 94 + 14v + v2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 14v + v2 = 0 + 94 14v + v2 = 0 + 94 Combine like terms: 0 + 94 = 94 14v + v2 = 94 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 = 94 + 49 Reorder the terms: 49 + 14v + v2 = 94 + 49 Combine like terms: 94 + 49 = 143 49 + 14v + v2 = 143 Factor a perfect square on the left side: (v + 7)(v + 7) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (v + 7) equal to 11.958260743 and -11.958260743.Subproblem 1
v + 7 = 11.958260743 Simplifying v + 7 = 11.958260743 Reorder the terms: 7 + v = 11.958260743 Solving 7 + v = 11.958260743 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 = 11.958260743 + -7 Combine like terms: 7 + -7 = 0 0 + v = 11.958260743 + -7 v = 11.958260743 + -7 Combine like terms: 11.958260743 + -7 = 4.958260743 v = 4.958260743 Simplifying v = 4.958260743Subproblem 2
v + 7 = -11.958260743 Simplifying v + 7 = -11.958260743 Reorder the terms: 7 + v = -11.958260743 Solving 7 + v = -11.958260743 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 = -11.958260743 + -7 Combine like terms: 7 + -7 = 0 0 + v = -11.958260743 + -7 v = -11.958260743 + -7 Combine like terms: -11.958260743 + -7 = -18.958260743 v = -18.958260743 Simplifying v = -18.958260743Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.958260743, -18.958260743}
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