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Simplifying 28v2 + 28v + -6 = 0 Reorder the terms: -6 + 28v + 28v2 = 0 Solving -6 + 28v + 28v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 14v + 14v2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 14v + 14v2)' equal to zero and attempt to solve: Simplifying -3 + 14v + 14v2 = 0 Solving -3 + 14v + 14v2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + v + v2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + v + 0.2142857143 + v2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + v + v2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + v + v2 = 0 + 0.2142857143 v + v2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 v + v2 = 0.2142857143 The v term is v. 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. + 0.25 + v2 = 0.2142857143 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + v2 = 0.2142857143 + 0.25 Combine like terms: 0.2142857143 + 0.25 = 0.4642857143 1.25 + v2 = 0.4642857143 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 0.4642857143 Calculate the square root of the right side: 0.681385144 Break this problem into two subproblems by setting (v + 0.5) equal to 0.681385144 and -0.681385144.Subproblem 1
v + 0.5 = 0.681385144 Simplifying v + 0.5 = 0.681385144 Reorder the terms: 0.5 + v = 0.681385144 Solving 0.5 + v = 0.681385144 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 = 0.681385144 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 0.681385144 + -0.5 v = 0.681385144 + -0.5 Combine like terms: 0.681385144 + -0.5 = 0.181385144 v = 0.181385144 Simplifying v = 0.181385144Subproblem 2
v + 0.5 = -0.681385144 Simplifying v + 0.5 = -0.681385144 Reorder the terms: 0.5 + v = -0.681385144 Solving 0.5 + v = -0.681385144 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 = -0.681385144 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -0.681385144 + -0.5 v = -0.681385144 + -0.5 Combine like terms: -0.681385144 + -0.5 = -1.181385144 v = -1.181385144 Simplifying v = -1.181385144Solution
The solution to the problem is based on the solutions from the subproblems. v = {0.181385144, -1.181385144}Solution
v = {0.181385144, -1.181385144}
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