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Simplifying (5U2 + -6U + -2) + (-4U + 1) = 0 Reorder the terms: (-2 + -6U + 5U2) + (-4U + 1) = 0 Remove parenthesis around (-2 + -6U + 5U2) -2 + -6U + 5U2 + (-4U + 1) = 0 Reorder the terms: -2 + -6U + 5U2 + (1 + -4U) = 0 Remove parenthesis around (1 + -4U) -2 + -6U + 5U2 + 1 + -4U = 0 Reorder the terms: -2 + 1 + -6U + -4U + 5U2 = 0 Combine like terms: -2 + 1 = -1 -1 + -6U + -4U + 5U2 = 0 Combine like terms: -6U + -4U = -10U -1 + -10U + 5U2 = 0 Solving -1 + -10U + 5U2 = 0 Solving for variable 'U'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -2U + U2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -2U + 0.2 + U2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -2U + U2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -2U + U2 = 0 + 0.2 -2U + U2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -2U + U2 = 0.2 The U term is -2U. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2U + 1 + U2 = 0.2 + 1 Reorder the terms: 1 + -2U + U2 = 0.2 + 1 Combine like terms: 0.2 + 1 = 1.2 1 + -2U + U2 = 1.2 Factor a perfect square on the left side: (U + -1)(U + -1) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (U + -1) equal to 1.095445115 and -1.095445115.Subproblem 1
U + -1 = 1.095445115 Simplifying U + -1 = 1.095445115 Reorder the terms: -1 + U = 1.095445115 Solving -1 + U = 1.095445115 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 + U = 1.095445115 + 1 Combine like terms: -1 + 1 = 0 0 + U = 1.095445115 + 1 U = 1.095445115 + 1 Combine like terms: 1.095445115 + 1 = 2.095445115 U = 2.095445115 Simplifying U = 2.095445115Subproblem 2
U + -1 = -1.095445115 Simplifying U + -1 = -1.095445115 Reorder the terms: -1 + U = -1.095445115 Solving -1 + U = -1.095445115 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 + U = -1.095445115 + 1 Combine like terms: -1 + 1 = 0 0 + U = -1.095445115 + 1 U = -1.095445115 + 1 Combine like terms: -1.095445115 + 1 = -0.095445115 U = -0.095445115 Simplifying U = -0.095445115Solution
The solution to the problem is based on the solutions from the subproblems. U = {2.095445115, -0.095445115}
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