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Simplifying v2 + 15v + -4050 = 0 Reorder the terms: -4050 + 15v + v2 = 0 Solving -4050 + 15v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '4050' to each side of the equation. -4050 + 15v + 4050 + v2 = 0 + 4050 Reorder the terms: -4050 + 4050 + 15v + v2 = 0 + 4050 Combine like terms: -4050 + 4050 = 0 0 + 15v + v2 = 0 + 4050 15v + v2 = 0 + 4050 Combine like terms: 0 + 4050 = 4050 15v + v2 = 4050 The v term is 15v. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15v + 56.25 + v2 = 4050 + 56.25 Reorder the terms: 56.25 + 15v + v2 = 4050 + 56.25 Combine like terms: 4050 + 56.25 = 4106.25 56.25 + 15v + v2 = 4106.25 Factor a perfect square on the left side: (v + 7.5)(v + 7.5) = 4106.25 Calculate the square root of the right side: 64.08002809 Break this problem into two subproblems by setting (v + 7.5) equal to 64.08002809 and -64.08002809.Subproblem 1
v + 7.5 = 64.08002809 Simplifying v + 7.5 = 64.08002809 Reorder the terms: 7.5 + v = 64.08002809 Solving 7.5 + v = 64.08002809 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = 64.08002809 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = 64.08002809 + -7.5 v = 64.08002809 + -7.5 Combine like terms: 64.08002809 + -7.5 = 56.58002809 v = 56.58002809 Simplifying v = 56.58002809Subproblem 2
v + 7.5 = -64.08002809 Simplifying v + 7.5 = -64.08002809 Reorder the terms: 7.5 + v = -64.08002809 Solving 7.5 + v = -64.08002809 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + v = -64.08002809 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + v = -64.08002809 + -7.5 v = -64.08002809 + -7.5 Combine like terms: -64.08002809 + -7.5 = -71.58002809 v = -71.58002809 Simplifying v = -71.58002809Solution
The solution to the problem is based on the solutions from the subproblems. v = {56.58002809, -71.58002809}
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