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Simplifying U2 + -4U = 3 Reorder the terms: -4U + U2 = 3 Solving -4U + U2 = 3 Solving for variable 'U'. Reorder the terms: -3 + -4U + U2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -4U + U2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -4U + 3 + U2 = 0 + 3 Reorder the terms: -3 + 3 + -4U + U2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4U + U2 = 0 + 3 -4U + U2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4U + U2 = 3 The U term is -4U. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4U + 4 + U2 = 3 + 4 Reorder the terms: 4 + -4U + U2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4U + U2 = 7 Factor a perfect square on the left side: (U + -2)(U + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (U + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
U + -2 = 2.645751311 Simplifying U + -2 = 2.645751311 Reorder the terms: -2 + U = 2.645751311 Solving -2 + U = 2.645751311 Solving for variable 'U'. Move all terms containing U to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + U = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + U = 2.645751311 + 2 U = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 U = 4.645751311 Simplifying U = 4.645751311Subproblem 2
U + -2 = -2.645751311 Simplifying U + -2 = -2.645751311 Reorder the terms: -2 + U = -2.645751311 Solving -2 + U = -2.645751311 Solving for variable 'U'. Move all terms containing U to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + U = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + U = -2.645751311 + 2 U = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 U = -0.645751311 Simplifying U = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. U = {4.645751311, -0.645751311}
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