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Simplifying 8v2 + 8v + -7 = 0 Reorder the terms: -7 + 8v + 8v2 = 0 Solving -7 + 8v + 8v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + v + v2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + v + 0.875 + v2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + v + v2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + v + v2 = 0 + 0.875 v + v2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 v + v2 = 0.875 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + v2 = 0.875 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 0.875 + 0.25 Combine like terms: 0.875 + 0.25 = 1.125 1.25 + v2 = 1.125 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (v + 0.5) equal to 1.060660172 and -1.060660172.Subproblem 1
v + 0.5 = 1.060660172 Simplifying v + 0.5 = 1.060660172 Reorder the terms: 0.5 + v = 1.060660172 Solving 0.5 + v = 1.060660172 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 1.060660172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 1.060660172 + -0.5 v = 1.060660172 + -0.5 Combine like terms: 1.060660172 + -0.5 = 0.560660172 v = 0.560660172 Simplifying v = 0.560660172Subproblem 2
v + 0.5 = -1.060660172 Simplifying v + 0.5 = -1.060660172 Reorder the terms: 0.5 + v = -1.060660172 Solving 0.5 + v = -1.060660172 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -1.060660172 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -1.060660172 + -0.5 v = -1.060660172 + -0.5 Combine like terms: -1.060660172 + -0.5 = -1.560660172 v = -1.560660172 Simplifying v = -1.560660172Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.560660172, -1.560660172}
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