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Simplifying 4v2 + -4v = 50 Reorder the terms: -4v + 4v2 = 50 Solving -4v + 4v2 = 50 Solving for variable 'v'. Reorder the terms: -50 + -4v + 4v2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -4v + 4v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -2v + 2v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -2v + 2v2)' equal to zero and attempt to solve: Simplifying -25 + -2v + 2v2 = 0 Solving -25 + -2v + 2v2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -1v + v2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1v + 12.5 + v2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1v + v2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1v + v2 = 0 + 12.5 -1v + v2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1v + v2 = 12.5 The v term is -1v. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1v + 0.25 + v2 = 12.5 + 0.25 Reorder the terms: 0.25 + -1v + v2 = 12.5 + 0.25 Combine like terms: 12.5 + 0.25 = 12.75 0.25 + -1v + v2 = 12.75 Factor a perfect square on the left side: (v + -0.5)(v + -0.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (v + -0.5) equal to 3.570714214 and -3.570714214.Subproblem 1
v + -0.5 = 3.570714214 Simplifying v + -0.5 = 3.570714214 Reorder the terms: -0.5 + v = 3.570714214 Solving -0.5 + v = 3.570714214 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 3.570714214 + 0.5 v = 3.570714214 + 0.5 Combine like terms: 3.570714214 + 0.5 = 4.070714214 v = 4.070714214 Simplifying v = 4.070714214Subproblem 2
v + -0.5 = -3.570714214 Simplifying v + -0.5 = -3.570714214 Reorder the terms: -0.5 + v = -3.570714214 Solving -0.5 + v = -3.570714214 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -3.570714214 + 0.5 v = -3.570714214 + 0.5 Combine like terms: -3.570714214 + 0.5 = -3.070714214 v = -3.070714214 Simplifying v = -3.070714214Solution
The solution to the problem is based on the solutions from the subproblems. v = {4.070714214, -3.070714214}Solution
v = {4.070714214, -3.070714214}
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