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Simplifying -6v2 + 42v + 12 = 0 Reorder the terms: 12 + 42v + -6v2 = 0 Solving 12 + 42v + -6v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6'. 6(2 + 7v + -1v2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + 7v + -1v2)' equal to zero and attempt to solve: Simplifying 2 + 7v + -1v2 = 0 Solving 2 + 7v + -1v2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -7v + v2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -7v + 2 + v2 = 0 + 2 Reorder the terms: -2 + 2 + -7v + v2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7v + v2 = 0 + 2 -7v + v2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7v + v2 = 2 The v term is -7v. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7v + 12.25 + v2 = 2 + 12.25 Reorder the terms: 12.25 + -7v + v2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + -7v + v2 = 14.25 Factor a perfect square on the left side: (v + -3.5)(v + -3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (v + -3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
v + -3.5 = 3.774917218 Simplifying v + -3.5 = 3.774917218 Reorder the terms: -3.5 + v = 3.774917218 Solving -3.5 + v = 3.774917218 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = 3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = 3.774917218 + 3.5 v = 3.774917218 + 3.5 Combine like terms: 3.774917218 + 3.5 = 7.274917218 v = 7.274917218 Simplifying v = 7.274917218Subproblem 2
v + -3.5 = -3.774917218 Simplifying v + -3.5 = -3.774917218 Reorder the terms: -3.5 + v = -3.774917218 Solving -3.5 + v = -3.774917218 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + v = -3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + v = -3.774917218 + 3.5 v = -3.774917218 + 3.5 Combine like terms: -3.774917218 + 3.5 = -0.274917218 v = -0.274917218 Simplifying v = -0.274917218Solution
The solution to the problem is based on the solutions from the subproblems. v = {7.274917218, -0.274917218}Solution
v = {7.274917218, -0.274917218}
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