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Simplifying 23u2 + -6u + -7 = 0 Reorder the terms: -7 + -6u + 23u2 = 0 Solving -7 + -6u + 23u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.3043478261 + -0.2608695652u + u2 = 0 Move the constant term to the right: Add '0.3043478261' to each side of the equation. -0.3043478261 + -0.2608695652u + 0.3043478261 + u2 = 0 + 0.3043478261 Reorder the terms: -0.3043478261 + 0.3043478261 + -0.2608695652u + u2 = 0 + 0.3043478261 Combine like terms: -0.3043478261 + 0.3043478261 = 0.0000000000 0.0000000000 + -0.2608695652u + u2 = 0 + 0.3043478261 -0.2608695652u + u2 = 0 + 0.3043478261 Combine like terms: 0 + 0.3043478261 = 0.3043478261 -0.2608695652u + u2 = 0.3043478261 The u term is -0.2608695652u. Take half its coefficient (-0.1304347826). Square it (0.01701323251) and add it to both sides. Add '0.01701323251' to each side of the equation. -0.2608695652u + 0.01701323251 + u2 = 0.3043478261 + 0.01701323251 Reorder the terms: 0.01701323251 + -0.2608695652u + u2 = 0.3043478261 + 0.01701323251 Combine like terms: 0.3043478261 + 0.01701323251 = 0.32136105861 0.01701323251 + -0.2608695652u + u2 = 0.32136105861 Factor a perfect square on the left side: (u + -0.1304347826)(u + -0.1304347826) = 0.32136105861 Calculate the square root of the right side: 0.566887166 Break this problem into two subproblems by setting (u + -0.1304347826) equal to 0.566887166 and -0.566887166.Subproblem 1
u + -0.1304347826 = 0.566887166 Simplifying u + -0.1304347826 = 0.566887166 Reorder the terms: -0.1304347826 + u = 0.566887166 Solving -0.1304347826 + u = 0.566887166 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.1304347826' to each side of the equation. -0.1304347826 + 0.1304347826 + u = 0.566887166 + 0.1304347826 Combine like terms: -0.1304347826 + 0.1304347826 = 0.0000000000 0.0000000000 + u = 0.566887166 + 0.1304347826 u = 0.566887166 + 0.1304347826 Combine like terms: 0.566887166 + 0.1304347826 = 0.6973219486 u = 0.6973219486 Simplifying u = 0.6973219486Subproblem 2
u + -0.1304347826 = -0.566887166 Simplifying u + -0.1304347826 = -0.566887166 Reorder the terms: -0.1304347826 + u = -0.566887166 Solving -0.1304347826 + u = -0.566887166 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.1304347826' to each side of the equation. -0.1304347826 + 0.1304347826 + u = -0.566887166 + 0.1304347826 Combine like terms: -0.1304347826 + 0.1304347826 = 0.0000000000 0.0000000000 + u = -0.566887166 + 0.1304347826 u = -0.566887166 + 0.1304347826 Combine like terms: -0.566887166 + 0.1304347826 = -0.4364523834 u = -0.4364523834 Simplifying u = -0.4364523834Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.6973219486, -0.4364523834}
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