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Simplifying 2(32u2 + -116u + -99) = 0 Reorder the terms: 2(-99 + -116u + 32u2) = 0 (-99 * 2 + -116u * 2 + 32u2 * 2) = 0 (-198 + -232u + 64u2) = 0 Solving -198 + -232u + 64u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + -116u + 32u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-99 + -116u + 32u2)' equal to zero and attempt to solve: Simplifying -99 + -116u + 32u2 = 0 Solving -99 + -116u + 32u2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -3.09375 + -3.625u + u2 = 0 Move the constant term to the right: Add '3.09375' to each side of the equation. -3.09375 + -3.625u + 3.09375 + u2 = 0 + 3.09375 Reorder the terms: -3.09375 + 3.09375 + -3.625u + u2 = 0 + 3.09375 Combine like terms: -3.09375 + 3.09375 = 0.00000 0.00000 + -3.625u + u2 = 0 + 3.09375 -3.625u + u2 = 0 + 3.09375 Combine like terms: 0 + 3.09375 = 3.09375 -3.625u + u2 = 3.09375 The u term is -3.625u. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625u + 3.28515625 + u2 = 3.09375 + 3.28515625 Reorder the terms: 3.28515625 + -3.625u + u2 = 3.09375 + 3.28515625 Combine like terms: 3.09375 + 3.28515625 = 6.37890625 3.28515625 + -3.625u + u2 = 6.37890625 Factor a perfect square on the left side: (u + -1.8125)(u + -1.8125) = 6.37890625 Calculate the square root of the right side: 2.525649669 Break this problem into two subproblems by setting (u + -1.8125) equal to 2.525649669 and -2.525649669.Subproblem 1
u + -1.8125 = 2.525649669 Simplifying u + -1.8125 = 2.525649669 Reorder the terms: -1.8125 + u = 2.525649669 Solving -1.8125 + u = 2.525649669 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + u = 2.525649669 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + u = 2.525649669 + 1.8125 u = 2.525649669 + 1.8125 Combine like terms: 2.525649669 + 1.8125 = 4.338149669 u = 4.338149669 Simplifying u = 4.338149669Subproblem 2
u + -1.8125 = -2.525649669 Simplifying u + -1.8125 = -2.525649669 Reorder the terms: -1.8125 + u = -2.525649669 Solving -1.8125 + u = -2.525649669 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + u = -2.525649669 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + u = -2.525649669 + 1.8125 u = -2.525649669 + 1.8125 Combine like terms: -2.525649669 + 1.8125 = -0.713149669 u = -0.713149669 Simplifying u = -0.713149669Solution
The solution to the problem is based on the solutions from the subproblems. u = {4.338149669, -0.713149669}Solution
u = {4.338149669, -0.713149669}
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