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Simplifying 8v2 + -21 = -8v Reorder the terms: -21 + 8v2 = -8v Solving -21 + 8v2 = -8v Solving for variable 'v'. Reorder the terms: -21 + 8v + 8v2 = -8v + 8v Combine like terms: -8v + 8v = 0 -21 + 8v + 8v2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.625 + v + v2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + v + 2.625 + v2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + v + v2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + v + v2 = 0 + 2.625 v + v2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 v + v2 = 2.625 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 = 2.625 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 2.625 + 0.25 Combine like terms: 2.625 + 0.25 = 2.875 1.25 + v2 = 2.875 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (v + 0.5) equal to 1.695582496 and -1.695582496.Subproblem 1
v + 0.5 = 1.695582496 Simplifying v + 0.5 = 1.695582496 Reorder the terms: 0.5 + v = 1.695582496 Solving 0.5 + v = 1.695582496 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 = 1.695582496 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 1.695582496 + -0.5 v = 1.695582496 + -0.5 Combine like terms: 1.695582496 + -0.5 = 1.195582496 v = 1.195582496 Simplifying v = 1.195582496Subproblem 2
v + 0.5 = -1.695582496 Simplifying v + 0.5 = -1.695582496 Reorder the terms: 0.5 + v = -1.695582496 Solving 0.5 + v = -1.695582496 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 = -1.695582496 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -1.695582496 + -0.5 v = -1.695582496 + -0.5 Combine like terms: -1.695582496 + -0.5 = -2.195582496 v = -2.195582496 Simplifying v = -2.195582496Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.195582496, -2.195582496}
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