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Simplifying 0 = 5v2 + -26v + -38 Reorder the terms: 0 = -38 + -26v + 5v2 Solving 0 = -38 + -26v + 5v2 Solving for variable 'v'. Combine like terms: 0 + 38 = 38 38 + 26v + -5v2 = -38 + -26v + 5v2 + 38 + 26v + -5v2 Reorder the terms: 38 + 26v + -5v2 = -38 + 38 + -26v + 26v + 5v2 + -5v2 Combine like terms: -38 + 38 = 0 38 + 26v + -5v2 = 0 + -26v + 26v + 5v2 + -5v2 38 + 26v + -5v2 = -26v + 26v + 5v2 + -5v2 Combine like terms: -26v + 26v = 0 38 + 26v + -5v2 = 0 + 5v2 + -5v2 38 + 26v + -5v2 = 5v2 + -5v2 Combine like terms: 5v2 + -5v2 = 0 38 + 26v + -5v2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -7.6 + -5.2v + v2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -5.2v + 7.6 + v2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -5.2v + v2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -5.2v + v2 = 0 + 7.6 -5.2v + v2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -5.2v + v2 = 7.6 The v term is -5.2v. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2v + 6.76 + v2 = 7.6 + 6.76 Reorder the terms: 6.76 + -5.2v + v2 = 7.6 + 6.76 Combine like terms: 7.6 + 6.76 = 14.36 6.76 + -5.2v + v2 = 14.36 Factor a perfect square on the left side: (v + -2.6)(v + -2.6) = 14.36 Calculate the square root of the right side: 3.789459064 Break this problem into two subproblems by setting (v + -2.6) equal to 3.789459064 and -3.789459064.Subproblem 1
v + -2.6 = 3.789459064 Simplifying v + -2.6 = 3.789459064 Reorder the terms: -2.6 + v = 3.789459064 Solving -2.6 + v = 3.789459064 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + v = 3.789459064 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = 3.789459064 + 2.6 v = 3.789459064 + 2.6 Combine like terms: 3.789459064 + 2.6 = 6.389459064 v = 6.389459064 Simplifying v = 6.389459064Subproblem 2
v + -2.6 = -3.789459064 Simplifying v + -2.6 = -3.789459064 Reorder the terms: -2.6 + v = -3.789459064 Solving -2.6 + v = -3.789459064 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + v = -3.789459064 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = -3.789459064 + 2.6 v = -3.789459064 + 2.6 Combine like terms: -3.789459064 + 2.6 = -1.189459064 v = -1.189459064 Simplifying v = -1.189459064Solution
The solution to the problem is based on the solutions from the subproblems. v = {6.389459064, -1.189459064}
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