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Simplifying (-12u6 + 20u3) + (-2u9 + 16u6) = 0 Reorder the terms: (20u3 + -12u6) + (-2u9 + 16u6) = 0 Remove parenthesis around (20u3 + -12u6) 20u3 + -12u6 + (-2u9 + 16u6) = 0 Reorder the terms: 20u3 + -12u6 + (16u6 + -2u9) = 0 Remove parenthesis around (16u6 + -2u9) 20u3 + -12u6 + 16u6 + -2u9 = 0 Combine like terms: -12u6 + 16u6 = 4u6 20u3 + 4u6 + -2u9 = 0 Solving 20u3 + 4u6 + -2u9 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2u3'. 2u3(10 + 2u3 + -1u6) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'u3' equal to zero and attempt to solve: Simplifying u3 = 0 Solving u3 = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u3 = 0 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 '(10 + 2u3 + -1u6)' equal to zero and attempt to solve: Simplifying 10 + 2u3 + -1u6 = 0 Solving 10 + 2u3 + -1u6 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -2u3 + u6 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -2u3 + 10 + u6 = 0 + 10 Reorder the terms: -10 + 10 + -2u3 + u6 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2u3 + u6 = 0 + 10 -2u3 + u6 = 0 + 10 Combine like terms: 0 + 10 = 10 -2u3 + u6 = 10 The u term is -2u3. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2u3 + 1 + u6 = 10 + 1 Reorder the terms: 1 + -2u3 + u6 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2u3 + u6 = 11 Factor a perfect square on the left side: (u3 + -1)(u3 + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (u3 + -1) equal to 3.31662479 and -3.31662479.Subproblem 1
u3 + -1 = 3.31662479 Simplifying u3 + -1 = 3.31662479 Reorder the terms: -1 + u3 = 3.31662479 Solving -1 + u3 = 3.31662479 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u3 = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + u3 = 3.31662479 + 1 u3 = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 u3 = 4.31662479 Simplifying u3 = 4.31662479 Reorder the terms: -4.31662479 + u3 = 4.31662479 + -4.31662479 Combine like terms: 4.31662479 + -4.31662479 = 0.00000000 -4.31662479 + u3 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
u3 + -1 = -3.31662479 Simplifying u3 + -1 = -3.31662479 Reorder the terms: -1 + u3 = -3.31662479 Solving -1 + u3 = -3.31662479 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + u3 = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + u3 = -3.31662479 + 1 u3 = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 u3 = -2.31662479 Simplifying u3 = -2.31662479 Reorder the terms: 2.31662479 + u3 = -2.31662479 + 2.31662479 Combine like terms: -2.31662479 + 2.31662479 = 0.00000000 2.31662479 + u3 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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