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Simplifying 5v(v + -2) + -3v = -4 Reorder the terms: 5v(-2 + v) + -3v = -4 (-2 * 5v + v * 5v) + -3v = -4 (-10v + 5v2) + -3v = -4 Reorder the terms: -10v + -3v + 5v2 = -4 Combine like terms: -10v + -3v = -13v -13v + 5v2 = -4 Solving -13v + 5v2 = -4 Solving for variable 'v'. Reorder the terms: 4 + -13v + 5v2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -13v + 5v2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -2.6v + v2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.6v + -0.8 + v2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.6v + v2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.6v + v2 = 0 + -0.8 -2.6v + v2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.6v + v2 = -0.8 The v term is -2.6v. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6v + 1.69 + v2 = -0.8 + 1.69 Reorder the terms: 1.69 + -2.6v + v2 = -0.8 + 1.69 Combine like terms: -0.8 + 1.69 = 0.89 1.69 + -2.6v + v2 = 0.89 Factor a perfect square on the left side: (v + -1.3)(v + -1.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (v + -1.3) equal to 0.943398113 and -0.943398113.Subproblem 1
v + -1.3 = 0.943398113 Simplifying v + -1.3 = 0.943398113 Reorder the terms: -1.3 + v = 0.943398113 Solving -1.3 + v = 0.943398113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + v = 0.943398113 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + v = 0.943398113 + 1.3 v = 0.943398113 + 1.3 Combine like terms: 0.943398113 + 1.3 = 2.243398113 v = 2.243398113 Simplifying v = 2.243398113Subproblem 2
v + -1.3 = -0.943398113 Simplifying v + -1.3 = -0.943398113 Reorder the terms: -1.3 + v = -0.943398113 Solving -1.3 + v = -0.943398113 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + v = -0.943398113 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + v = -0.943398113 + 1.3 v = -0.943398113 + 1.3 Combine like terms: -0.943398113 + 1.3 = 0.356601887 v = 0.356601887 Simplifying v = 0.356601887Solution
The solution to the problem is based on the solutions from the subproblems. v = {2.243398113, 0.356601887}
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