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Simplifying 8v2 + -15v + -18 = 0 Reorder the terms: -18 + -15v + 8v2 = 0 Solving -18 + -15v + 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'. -2.25 + -1.875v + v2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.875v + 2.25 + v2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.875v + v2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.875v + v2 = 0 + 2.25 -1.875v + v2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1.875v + v2 = 2.25 The v term is -1.875v. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875v + 0.87890625 + v2 = 2.25 + 0.87890625 Reorder the terms: 0.87890625 + -1.875v + v2 = 2.25 + 0.87890625 Combine like terms: 2.25 + 0.87890625 = 3.12890625 0.87890625 + -1.875v + v2 = 3.12890625 Factor a perfect square on the left side: (v + -0.9375)(v + -0.9375) = 3.12890625 Calculate the square root of the right side: 1.768871462 Break this problem into two subproblems by setting (v + -0.9375) equal to 1.768871462 and -1.768871462.Subproblem 1
v + -0.9375 = 1.768871462 Simplifying v + -0.9375 = 1.768871462 Reorder the terms: -0.9375 + v = 1.768871462 Solving -0.9375 + v = 1.768871462 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + v = 1.768871462 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + v = 1.768871462 + 0.9375 v = 1.768871462 + 0.9375 Combine like terms: 1.768871462 + 0.9375 = 2.706371462 v = 2.706371462 Simplifying v = 2.706371462Subproblem 2
v + -0.9375 = -1.768871462 Simplifying v + -0.9375 = -1.768871462 Reorder the terms: -0.9375 + v = -1.768871462 Solving -0.9375 + v = -1.768871462 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + v = -1.768871462 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + v = -1.768871462 + 0.9375 v = -1.768871462 + 0.9375 Combine like terms: -1.768871462 + 0.9375 = -0.831371462 v = -0.831371462 Simplifying v = -0.831371462Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.706371462, -0.831371462}
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