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Simplifying v2 + 6v + -53 = 0 Reorder the terms: -53 + 6v + v2 = 0 Solving -53 + 6v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 6v + 53 + v2 = 0 + 53 Reorder the terms: -53 + 53 + 6v + v2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 6v + v2 = 0 + 53 6v + v2 = 0 + 53 Combine like terms: 0 + 53 = 53 6v + v2 = 53 The v term is 6v. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6v + 9 + v2 = 53 + 9 Reorder the terms: 9 + 6v + v2 = 53 + 9 Combine like terms: 53 + 9 = 62 9 + 6v + v2 = 62 Factor a perfect square on the left side: (v + 3)(v + 3) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (v + 3) equal to 7.874007874 and -7.874007874.Subproblem 1
v + 3 = 7.874007874 Simplifying v + 3 = 7.874007874 Reorder the terms: 3 + v = 7.874007874 Solving 3 + v = 7.874007874 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = 7.874007874 + -3 Combine like terms: 3 + -3 = 0 0 + v = 7.874007874 + -3 v = 7.874007874 + -3 Combine like terms: 7.874007874 + -3 = 4.874007874 v = 4.874007874 Simplifying v = 4.874007874Subproblem 2
v + 3 = -7.874007874 Simplifying v + 3 = -7.874007874 Reorder the terms: 3 + v = -7.874007874 Solving 3 + v = -7.874007874 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = -7.874007874 + -3 Combine like terms: 3 + -3 = 0 0 + v = -7.874007874 + -3 v = -7.874007874 + -3 Combine like terms: -7.874007874 + -3 = -10.874007874 v = -10.874007874 Simplifying v = -10.874007874Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.874007874, -10.874007874}
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