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Simplifying (v2 + -7v + -3) + (4v2 + -5v + 6) = 0 Reorder the terms: (-3 + -7v + v2) + (4v2 + -5v + 6) = 0 Remove parenthesis around (-3 + -7v + v2) -3 + -7v + v2 + (4v2 + -5v + 6) = 0 Reorder the terms: -3 + -7v + v2 + (6 + -5v + 4v2) = 0 Remove parenthesis around (6 + -5v + 4v2) -3 + -7v + v2 + 6 + -5v + 4v2 = 0 Reorder the terms: -3 + 6 + -7v + -5v + v2 + 4v2 = 0 Combine like terms: -3 + 6 = 3 3 + -7v + -5v + v2 + 4v2 = 0 Combine like terms: -7v + -5v = -12v 3 + -12v + v2 + 4v2 = 0 Combine like terms: v2 + 4v2 = 5v2 3 + -12v + 5v2 = 0 Solving 3 + -12v + 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'. 0.6 + -2.4v + v2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.4v + -0.6 + v2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.4v + v2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.4v + v2 = 0 + -0.6 -2.4v + v2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.4v + v2 = -0.6 The v term is -2.4v. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4v + 1.44 + v2 = -0.6 + 1.44 Reorder the terms: 1.44 + -2.4v + v2 = -0.6 + 1.44 Combine like terms: -0.6 + 1.44 = 0.84 1.44 + -2.4v + v2 = 0.84 Factor a perfect square on the left side: (v + -1.2)(v + -1.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (v + -1.2) equal to 0.916515139 and -0.916515139.Subproblem 1
v + -1.2 = 0.916515139 Simplifying v + -1.2 = 0.916515139 Reorder the terms: -1.2 + v = 0.916515139 Solving -1.2 + v = 0.916515139 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + v = 0.916515139 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + v = 0.916515139 + 1.2 v = 0.916515139 + 1.2 Combine like terms: 0.916515139 + 1.2 = 2.116515139 v = 2.116515139 Simplifying v = 2.116515139Subproblem 2
v + -1.2 = -0.916515139 Simplifying v + -1.2 = -0.916515139 Reorder the terms: -1.2 + v = -0.916515139 Solving -1.2 + v = -0.916515139 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + v = -0.916515139 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + v = -0.916515139 + 1.2 v = -0.916515139 + 1.2 Combine like terms: -0.916515139 + 1.2 = 0.283484861 v = 0.283484861 Simplifying v = 0.283484861Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.116515139, 0.283484861}
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