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Simplifying 5u2 = 7u + 3 Reorder the terms: 5u2 = 3 + 7u Solving 5u2 = 3 + 7u Solving for variable 'u'. Reorder the terms: -3 + -7u + 5u2 = 3 + 7u + -3 + -7u Reorder the terms: -3 + -7u + 5u2 = 3 + -3 + 7u + -7u Combine like terms: 3 + -3 = 0 -3 + -7u + 5u2 = 0 + 7u + -7u -3 + -7u + 5u2 = 7u + -7u Combine like terms: 7u + -7u = 0 -3 + -7u + 5u2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.4u + u2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.4u + 0.6 + u2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.4u + u2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.4u + u2 = 0 + 0.6 -1.4u + u2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.4u + u2 = 0.6 The u term is -1.4u. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4u + 0.49 + u2 = 0.6 + 0.49 Reorder the terms: 0.49 + -1.4u + u2 = 0.6 + 0.49 Combine like terms: 0.6 + 0.49 = 1.09 0.49 + -1.4u + u2 = 1.09 Factor a perfect square on the left side: (u + -0.7)(u + -0.7) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (u + -0.7) equal to 1.044030651 and -1.044030651.Subproblem 1
u + -0.7 = 1.044030651 Simplifying u + -0.7 = 1.044030651 Reorder the terms: -0.7 + u = 1.044030651 Solving -0.7 + u = 1.044030651 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + u = 1.044030651 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + u = 1.044030651 + 0.7 u = 1.044030651 + 0.7 Combine like terms: 1.044030651 + 0.7 = 1.744030651 u = 1.744030651 Simplifying u = 1.744030651Subproblem 2
u + -0.7 = -1.044030651 Simplifying u + -0.7 = -1.044030651 Reorder the terms: -0.7 + u = -1.044030651 Solving -0.7 + u = -1.044030651 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + u = -1.044030651 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + u = -1.044030651 + 0.7 u = -1.044030651 + 0.7 Combine like terms: -1.044030651 + 0.7 = -0.344030651 u = -0.344030651 Simplifying u = -0.344030651Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.744030651, -0.344030651}
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