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Simplifying 7v2 + -49 = -35v Reorder the terms: -49 + 7v2 = -35v Solving -49 + 7v2 = -35v Solving for variable 'v'. Reorder the terms: -49 + 35v + 7v2 = -35v + 35v Combine like terms: -35v + 35v = 0 -49 + 35v + 7v2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-7 + 5v + v2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-7 + 5v + v2)' equal to zero and attempt to solve: Simplifying -7 + 5v + v2 = 0 Solving -7 + 5v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 5v + 7 + v2 = 0 + 7 Reorder the terms: -7 + 7 + 5v + v2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5v + v2 = 0 + 7 5v + v2 = 0 + 7 Combine like terms: 0 + 7 = 7 5v + v2 = 7 The v term is 5v. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5v + 6.25 + v2 = 7 + 6.25 Reorder the terms: 6.25 + 5v + v2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + 5v + v2 = 13.25 Factor a perfect square on the left side: (v + 2.5)(v + 2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (v + 2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
v + 2.5 = 3.640054945 Simplifying v + 2.5 = 3.640054945 Reorder the terms: 2.5 + v = 3.640054945 Solving 2.5 + v = 3.640054945 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = 3.640054945 + -2.5 v = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 v = 1.140054945 Simplifying v = 1.140054945Subproblem 2
v + 2.5 = -3.640054945 Simplifying v + 2.5 = -3.640054945 Reorder the terms: 2.5 + v = -3.640054945 Solving 2.5 + v = -3.640054945 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + v = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + v = -3.640054945 + -2.5 v = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 v = -6.140054945 Simplifying v = -6.140054945Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.140054945, -6.140054945}Solution
v = {1.140054945, -6.140054945}
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