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Simplifying v2 + -25v + 29 = 0 Reorder the terms: 29 + -25v + v2 = 0 Solving 29 + -25v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -25v + -29 + v2 = 0 + -29 Reorder the terms: 29 + -29 + -25v + v2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -25v + v2 = 0 + -29 -25v + v2 = 0 + -29 Combine like terms: 0 + -29 = -29 -25v + v2 = -29 The v term is -25v. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25v + 156.25 + v2 = -29 + 156.25 Reorder the terms: 156.25 + -25v + v2 = -29 + 156.25 Combine like terms: -29 + 156.25 = 127.25 156.25 + -25v + v2 = 127.25 Factor a perfect square on the left side: (v + -12.5)(v + -12.5) = 127.25 Calculate the square root of the right side: 11.280514173 Break this problem into two subproblems by setting (v + -12.5) equal to 11.280514173 and -11.280514173.Subproblem 1
v + -12.5 = 11.280514173 Simplifying v + -12.5 = 11.280514173 Reorder the terms: -12.5 + v = 11.280514173 Solving -12.5 + v = 11.280514173 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + v = 11.280514173 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + v = 11.280514173 + 12.5 v = 11.280514173 + 12.5 Combine like terms: 11.280514173 + 12.5 = 23.780514173 v = 23.780514173 Simplifying v = 23.780514173Subproblem 2
v + -12.5 = -11.280514173 Simplifying v + -12.5 = -11.280514173 Reorder the terms: -12.5 + v = -11.280514173 Solving -12.5 + v = -11.280514173 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + v = -11.280514173 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + v = -11.280514173 + 12.5 v = -11.280514173 + 12.5 Combine like terms: -11.280514173 + 12.5 = 1.219485827 v = 1.219485827 Simplifying v = 1.219485827Solution
The solution to the problem is based on the solutions from the subproblems. v = {23.780514173, 1.219485827}
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