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Simplifying 10v2 = 18v + 3 Reorder the terms: 10v2 = 3 + 18v Solving 10v2 = 3 + 18v Solving for variable 'v'. Reorder the terms: -3 + -18v + 10v2 = 3 + 18v + -3 + -18v Reorder the terms: -3 + -18v + 10v2 = 3 + -3 + 18v + -18v Combine like terms: 3 + -3 = 0 -3 + -18v + 10v2 = 0 + 18v + -18v -3 + -18v + 10v2 = 18v + -18v Combine like terms: 18v + -18v = 0 -3 + -18v + 10v2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -1.8v + v2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.8v + 0.3 + v2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.8v + v2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.8v + v2 = 0 + 0.3 -1.8v + v2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -1.8v + v2 = 0.3 The v term is -1.8v. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8v + 0.81 + v2 = 0.3 + 0.81 Reorder the terms: 0.81 + -1.8v + v2 = 0.3 + 0.81 Combine like terms: 0.3 + 0.81 = 1.11 0.81 + -1.8v + v2 = 1.11 Factor a perfect square on the left side: (v + -0.9)(v + -0.9) = 1.11 Calculate the square root of the right side: 1.053565375 Break this problem into two subproblems by setting (v + -0.9) equal to 1.053565375 and -1.053565375.Subproblem 1
v + -0.9 = 1.053565375 Simplifying v + -0.9 = 1.053565375 Reorder the terms: -0.9 + v = 1.053565375 Solving -0.9 + v = 1.053565375 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + v = 1.053565375 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + v = 1.053565375 + 0.9 v = 1.053565375 + 0.9 Combine like terms: 1.053565375 + 0.9 = 1.953565375 v = 1.953565375 Simplifying v = 1.953565375Subproblem 2
v + -0.9 = -1.053565375 Simplifying v + -0.9 = -1.053565375 Reorder the terms: -0.9 + v = -1.053565375 Solving -0.9 + v = -1.053565375 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + v = -1.053565375 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + v = -1.053565375 + 0.9 v = -1.053565375 + 0.9 Combine like terms: -1.053565375 + 0.9 = -0.153565375 v = -0.153565375 Simplifying v = -0.153565375Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.953565375, -0.153565375}
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