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Simplifying 10v2 + 6v + -13 = 0 Reorder the terms: -13 + 6v + 10v2 = 0 Solving -13 + 6v + 10v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.3 + 0.6v + v2 = 0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + 0.6v + 1.3 + v2 = 0 + 1.3 Reorder the terms: -1.3 + 1.3 + 0.6v + v2 = 0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + 0.6v + v2 = 0 + 1.3 0.6v + v2 = 0 + 1.3 Combine like terms: 0 + 1.3 = 1.3 0.6v + v2 = 1.3 The v term is 0.6v. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6v + 0.09 + v2 = 1.3 + 0.09 Reorder the terms: 0.09 + 0.6v + v2 = 1.3 + 0.09 Combine like terms: 1.3 + 0.09 = 1.39 0.09 + 0.6v + v2 = 1.39 Factor a perfect square on the left side: (v + 0.3)(v + 0.3) = 1.39 Calculate the square root of the right side: 1.178982612 Break this problem into two subproblems by setting (v + 0.3) equal to 1.178982612 and -1.178982612.Subproblem 1
v + 0.3 = 1.178982612 Simplifying v + 0.3 = 1.178982612 Reorder the terms: 0.3 + v = 1.178982612 Solving 0.3 + v = 1.178982612 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + v = 1.178982612 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + v = 1.178982612 + -0.3 v = 1.178982612 + -0.3 Combine like terms: 1.178982612 + -0.3 = 0.878982612 v = 0.878982612 Simplifying v = 0.878982612Subproblem 2
v + 0.3 = -1.178982612 Simplifying v + 0.3 = -1.178982612 Reorder the terms: 0.3 + v = -1.178982612 Solving 0.3 + v = -1.178982612 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + v = -1.178982612 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + v = -1.178982612 + -0.3 v = -1.178982612 + -0.3 Combine like terms: -1.178982612 + -0.3 = -1.478982612 v = -1.478982612 Simplifying v = -1.478982612Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.878982612, -1.478982612}
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