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Simplifying -2v2 + 7v + 8 = 0 Reorder the terms: 8 + 7v + -2v2 = 0 Solving 8 + 7v + -2v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4 + -3.5v + v2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.5v + 4 + v2 = 0 + 4 Reorder the terms: -4 + 4 + -3.5v + v2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.5v + v2 = 0 + 4 -3.5v + v2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.5v + v2 = 4 The v term is -3.5v. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5v + 3.0625 + v2 = 4 + 3.0625 Reorder the terms: 3.0625 + -3.5v + v2 = 4 + 3.0625 Combine like terms: 4 + 3.0625 = 7.0625 3.0625 + -3.5v + v2 = 7.0625 Factor a perfect square on the left side: (v + -1.75)(v + -1.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (v + -1.75) equal to 2.657536453 and -2.657536453.Subproblem 1
v + -1.75 = 2.657536453 Simplifying v + -1.75 = 2.657536453 Reorder the terms: -1.75 + v = 2.657536453 Solving -1.75 + v = 2.657536453 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + v = 2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + v = 2.657536453 + 1.75 v = 2.657536453 + 1.75 Combine like terms: 2.657536453 + 1.75 = 4.407536453 v = 4.407536453 Simplifying v = 4.407536453Subproblem 2
v + -1.75 = -2.657536453 Simplifying v + -1.75 = -2.657536453 Reorder the terms: -1.75 + v = -2.657536453 Solving -1.75 + v = -2.657536453 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + v = -2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + v = -2.657536453 + 1.75 v = -2.657536453 + 1.75 Combine like terms: -2.657536453 + 1.75 = -0.907536453 v = -0.907536453 Simplifying v = -0.907536453Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.407536453, -0.907536453}
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