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Simplifying 2u2v + -18uv = 28v Reorder the terms: -18uv + 2u2v = 28v Solving -18uv + 2u2v = 28v Solving for variable 'u'. Combine like terms: 28v + -28v = 0 -18uv + 2u2v + -28v = 0 Factor out the Greatest Common Factor (GCF), '2v'. 2v(-9u + u2 + -14) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. v + -1v = 0 + -1v Remove the zero: 0 = -1v Simplifying 0 = -1v The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-9u + u2 + -14)' equal to zero and attempt to solve: Simplifying -9u + u2 + -14 = 0 Reorder the terms: -14 + -9u + u2 = 0 Solving -14 + -9u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -9u + 14 + u2 = 0 + 14 Reorder the terms: -14 + 14 + -9u + u2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -9u + u2 = 0 + 14 -9u + u2 = 0 + 14 Combine like terms: 0 + 14 = 14 -9u + u2 = 14 The u term is -9u. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9u + 20.25 + u2 = 14 + 20.25 Reorder the terms: 20.25 + -9u + u2 = 14 + 20.25 Combine like terms: 14 + 20.25 = 34.25 20.25 + -9u + u2 = 34.25 Factor a perfect square on the left side: (u + -4.5)(u + -4.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (u + -4.5) equal to 5.852349955 and -5.852349955.Subproblem 1
u + -4.5 = 5.852349955 Simplifying u + -4.5 = 5.852349955 Reorder the terms: -4.5 + u = 5.852349955 Solving -4.5 + u = 5.852349955 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + u = 5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = 5.852349955 + 4.5 u = 5.852349955 + 4.5 Combine like terms: 5.852349955 + 4.5 = 10.352349955 u = 10.352349955 Simplifying u = 10.352349955Subproblem 2
u + -4.5 = -5.852349955 Simplifying u + -4.5 = -5.852349955 Reorder the terms: -4.5 + u = -5.852349955 Solving -4.5 + u = -5.852349955 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + u = -5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + u = -5.852349955 + 4.5 u = -5.852349955 + 4.5 Combine like terms: -5.852349955 + 4.5 = -1.352349955 u = -1.352349955 Simplifying u = -1.352349955Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.352349955, -1.352349955}Solution
u = {10.352349955, -1.352349955}
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