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Simplifying v2 + -10v + -28 = 9 Reorder the terms: -28 + -10v + v2 = 9 Solving -28 + -10v + v2 = 9 Solving for variable 'v'. Reorder the terms: -28 + -9 + -10v + v2 = 9 + -9 Combine like terms: -28 + -9 = -37 -37 + -10v + v2 = 9 + -9 Combine like terms: 9 + -9 = 0 -37 + -10v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -10v + 37 + v2 = 0 + 37 Reorder the terms: -37 + 37 + -10v + v2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -10v + v2 = 0 + 37 -10v + v2 = 0 + 37 Combine like terms: 0 + 37 = 37 -10v + v2 = 37 The v term is -10v. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10v + 25 + v2 = 37 + 25 Reorder the terms: 25 + -10v + v2 = 37 + 25 Combine like terms: 37 + 25 = 62 25 + -10v + v2 = 62 Factor a perfect square on the left side: (v + -5)(v + -5) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (v + -5) equal to 7.874007874 and -7.874007874.Subproblem 1
v + -5 = 7.874007874 Simplifying v + -5 = 7.874007874 Reorder the terms: -5 + v = 7.874007874 Solving -5 + v = 7.874007874 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = 7.874007874 + 5 Combine like terms: -5 + 5 = 0 0 + v = 7.874007874 + 5 v = 7.874007874 + 5 Combine like terms: 7.874007874 + 5 = 12.874007874 v = 12.874007874 Simplifying v = 12.874007874Subproblem 2
v + -5 = -7.874007874 Simplifying v + -5 = -7.874007874 Reorder the terms: -5 + v = -7.874007874 Solving -5 + v = -7.874007874 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + v = -7.874007874 + 5 Combine like terms: -5 + 5 = 0 0 + v = -7.874007874 + 5 v = -7.874007874 + 5 Combine like terms: -7.874007874 + 5 = -2.874007874 v = -2.874007874 Simplifying v = -2.874007874Solution
The solution to the problem is based on the solutions from the subproblems. v = {12.874007874, -2.874007874}
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