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Simplifying v2 + 7v + -56 = 0 Reorder the terms: -56 + 7v + v2 = 0 Solving -56 + 7v + v2 = 0 Solving for variable 'v'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 7v + 56 + v2 = 0 + 56 Reorder the terms: -56 + 56 + 7v + v2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 7v + v2 = 0 + 56 7v + v2 = 0 + 56 Combine like terms: 0 + 56 = 56 7v + v2 = 56 The v term is 7v. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7v + 12.25 + v2 = 56 + 12.25 Reorder the terms: 12.25 + 7v + v2 = 56 + 12.25 Combine like terms: 56 + 12.25 = 68.25 12.25 + 7v + v2 = 68.25 Factor a perfect square on the left side: (v + 3.5)(v + 3.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (v + 3.5) equal to 8.261355821 and -8.261355821.Subproblem 1
v + 3.5 = 8.261355821 Simplifying v + 3.5 = 8.261355821 Reorder the terms: 3.5 + v = 8.261355821 Solving 3.5 + v = 8.261355821 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = 8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = 8.261355821 + -3.5 v = 8.261355821 + -3.5 Combine like terms: 8.261355821 + -3.5 = 4.761355821 v = 4.761355821 Simplifying v = 4.761355821Subproblem 2
v + 3.5 = -8.261355821 Simplifying v + 3.5 = -8.261355821 Reorder the terms: 3.5 + v = -8.261355821 Solving 3.5 + v = -8.261355821 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + v = -8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + v = -8.261355821 + -3.5 v = -8.261355821 + -3.5 Combine like terms: -8.261355821 + -3.5 = -11.761355821 v = -11.761355821 Simplifying v = -11.761355821Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.761355821, -11.761355821}
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