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Simplifying 0 = 5v2 + -26v + -99 Reorder the terms: 0 = -99 + -26v + 5v2 Solving 0 = -99 + -26v + 5v2 Solving for variable 'v'. Combine like terms: 0 + 99 = 99 99 + 26v + -5v2 = -99 + -26v + 5v2 + 99 + 26v + -5v2 Reorder the terms: 99 + 26v + -5v2 = -99 + 99 + -26v + 26v + 5v2 + -5v2 Combine like terms: -99 + 99 = 0 99 + 26v + -5v2 = 0 + -26v + 26v + 5v2 + -5v2 99 + 26v + -5v2 = -26v + 26v + 5v2 + -5v2 Combine like terms: -26v + 26v = 0 99 + 26v + -5v2 = 0 + 5v2 + -5v2 99 + 26v + -5v2 = 5v2 + -5v2 Combine like terms: 5v2 + -5v2 = 0 99 + 26v + -5v2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -19.8 + -5.2v + v2 = 0 Move the constant term to the right: Add '19.8' to each side of the equation. -19.8 + -5.2v + 19.8 + v2 = 0 + 19.8 Reorder the terms: -19.8 + 19.8 + -5.2v + v2 = 0 + 19.8 Combine like terms: -19.8 + 19.8 = 0.0 0.0 + -5.2v + v2 = 0 + 19.8 -5.2v + v2 = 0 + 19.8 Combine like terms: 0 + 19.8 = 19.8 -5.2v + v2 = 19.8 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 = 19.8 + 6.76 Reorder the terms: 6.76 + -5.2v + v2 = 19.8 + 6.76 Combine like terms: 19.8 + 6.76 = 26.56 6.76 + -5.2v + v2 = 26.56 Factor a perfect square on the left side: (v + -2.6)(v + -2.6) = 26.56 Calculate the square root of the right side: 5.153639491 Break this problem into two subproblems by setting (v + -2.6) equal to 5.153639491 and -5.153639491.Subproblem 1
v + -2.6 = 5.153639491 Simplifying v + -2.6 = 5.153639491 Reorder the terms: -2.6 + v = 5.153639491 Solving -2.6 + v = 5.153639491 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 = 5.153639491 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = 5.153639491 + 2.6 v = 5.153639491 + 2.6 Combine like terms: 5.153639491 + 2.6 = 7.753639491 v = 7.753639491 Simplifying v = 7.753639491Subproblem 2
v + -2.6 = -5.153639491 Simplifying v + -2.6 = -5.153639491 Reorder the terms: -2.6 + v = -5.153639491 Solving -2.6 + v = -5.153639491 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 = -5.153639491 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + v = -5.153639491 + 2.6 v = -5.153639491 + 2.6 Combine like terms: -5.153639491 + 2.6 = -2.553639491 v = -2.553639491 Simplifying v = -2.553639491Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.753639491, -2.553639491}
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