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Simplifying 5v2 + -7v + -1 = 0 Reorder the terms: -1 + -7v + 5v2 = 0 Solving -1 + -7v + 5v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -1.4v + v2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.4v + 0.2 + v2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.4v + v2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.4v + v2 = 0 + 0.2 -1.4v + v2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.4v + v2 = 0.2 The v term is -1.4v. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4v + 0.49 + v2 = 0.2 + 0.49 Reorder the terms: 0.49 + -1.4v + v2 = 0.2 + 0.49 Combine like terms: 0.2 + 0.49 = 0.69 0.49 + -1.4v + v2 = 0.69 Factor a perfect square on the left side: (v + -0.7)(v + -0.7) = 0.69 Calculate the square root of the right side: 0.830662386 Break this problem into two subproblems by setting (v + -0.7) equal to 0.830662386 and -0.830662386.Subproblem 1
v + -0.7 = 0.830662386 Simplifying v + -0.7 = 0.830662386 Reorder the terms: -0.7 + v = 0.830662386 Solving -0.7 + v = 0.830662386 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + v = 0.830662386 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + v = 0.830662386 + 0.7 v = 0.830662386 + 0.7 Combine like terms: 0.830662386 + 0.7 = 1.530662386 v = 1.530662386 Simplifying v = 1.530662386Subproblem 2
v + -0.7 = -0.830662386 Simplifying v + -0.7 = -0.830662386 Reorder the terms: -0.7 + v = -0.830662386 Solving -0.7 + v = -0.830662386 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + v = -0.830662386 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + v = -0.830662386 + 0.7 v = -0.830662386 + 0.7 Combine like terms: -0.830662386 + 0.7 = -0.130662386 v = -0.130662386 Simplifying v = -0.130662386Solution
The solution to the problem is based on the solutions from the subproblems. v = {1.530662386, -0.130662386}
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