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Simplifying v2 + -26v = 47 Reorder the terms: -26v + v2 = 47 Solving -26v + v2 = 47 Solving for variable 'v'. Reorder the terms: -47 + -26v + v2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + -26v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -26v + 47 + v2 = 0 + 47 Reorder the terms: -47 + 47 + -26v + v2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -26v + v2 = 0 + 47 -26v + v2 = 0 + 47 Combine like terms: 0 + 47 = 47 -26v + v2 = 47 The v term is -26v. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26v + 169 + v2 = 47 + 169 Reorder the terms: 169 + -26v + v2 = 47 + 169 Combine like terms: 47 + 169 = 216 169 + -26v + v2 = 216 Factor a perfect square on the left side: (v + -13)(v + -13) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (v + -13) equal to 14.696938457 and -14.696938457.Subproblem 1
v + -13 = 14.696938457 Simplifying v + -13 = 14.696938457 Reorder the terms: -13 + v = 14.696938457 Solving -13 + v = 14.696938457 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = 14.696938457 + 13 Combine like terms: -13 + 13 = 0 0 + v = 14.696938457 + 13 v = 14.696938457 + 13 Combine like terms: 14.696938457 + 13 = 27.696938457 v = 27.696938457 Simplifying v = 27.696938457Subproblem 2
v + -13 = -14.696938457 Simplifying v + -13 = -14.696938457 Reorder the terms: -13 + v = -14.696938457 Solving -13 + v = -14.696938457 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + v = -14.696938457 + 13 Combine like terms: -13 + 13 = 0 0 + v = -14.696938457 + 13 v = -14.696938457 + 13 Combine like terms: -14.696938457 + 13 = -1.696938457 v = -1.696938457 Simplifying v = -1.696938457Solution
The solution to the problem is based on the solutions from the subproblems. v = {27.696938457, -1.696938457}
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