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Simplifying v2 + -14v + -59 = -4 Reorder the terms: -59 + -14v + v2 = -4 Solving -59 + -14v + v2 = -4 Solving for variable 'v'. Reorder the terms: -59 + 4 + -14v + v2 = -4 + 4 Combine like terms: -59 + 4 = -55 -55 + -14v + v2 = -4 + 4 Combine like terms: -4 + 4 = 0 -55 + -14v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -14v + 55 + v2 = 0 + 55 Reorder the terms: -55 + 55 + -14v + v2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -14v + v2 = 0 + 55 -14v + v2 = 0 + 55 Combine like terms: 0 + 55 = 55 -14v + v2 = 55 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 = 55 + 49 Reorder the terms: 49 + -14v + v2 = 55 + 49 Combine like terms: 55 + 49 = 104 49 + -14v + v2 = 104 Factor a perfect square on the left side: (v + -7)(v + -7) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (v + -7) equal to 10.198039027 and -10.198039027.Subproblem 1
v + -7 = 10.198039027 Simplifying v + -7 = 10.198039027 Reorder the terms: -7 + v = 10.198039027 Solving -7 + v = 10.198039027 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 = 10.198039027 + 7 Combine like terms: -7 + 7 = 0 0 + v = 10.198039027 + 7 v = 10.198039027 + 7 Combine like terms: 10.198039027 + 7 = 17.198039027 v = 17.198039027 Simplifying v = 17.198039027Subproblem 2
v + -7 = -10.198039027 Simplifying v + -7 = -10.198039027 Reorder the terms: -7 + v = -10.198039027 Solving -7 + v = -10.198039027 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 = -10.198039027 + 7 Combine like terms: -7 + 7 = 0 0 + v = -10.198039027 + 7 v = -10.198039027 + 7 Combine like terms: -10.198039027 + 7 = -3.198039027 v = -3.198039027 Simplifying v = -3.198039027Solution
The solution to the problem is based on the solutions from the subproblems. v = {17.198039027, -3.198039027}
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