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Simplifying U2 + 3U + -91 = 0 Reorder the terms: -91 + 3U + U2 = 0 Solving -91 + 3U + U2 = 0 Solving for variable 'U'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 3U + 91 + U2 = 0 + 91 Reorder the terms: -91 + 91 + 3U + U2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 3U + U2 = 0 + 91 3U + U2 = 0 + 91 Combine like terms: 0 + 91 = 91 3U + U2 = 91 The U term is 3U. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3U + 2.25 + U2 = 91 + 2.25 Reorder the terms: 2.25 + 3U + U2 = 91 + 2.25 Combine like terms: 91 + 2.25 = 93.25 2.25 + 3U + U2 = 93.25 Factor a perfect square on the left side: (U + 1.5)(U + 1.5) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (U + 1.5) equal to 9.656603958 and -9.656603958.Subproblem 1
U + 1.5 = 9.656603958 Simplifying U + 1.5 = 9.656603958 Reorder the terms: 1.5 + U = 9.656603958 Solving 1.5 + U = 9.656603958 Solving for variable 'U'. Move all terms containing U to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + U = 9.656603958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + U = 9.656603958 + -1.5 U = 9.656603958 + -1.5 Combine like terms: 9.656603958 + -1.5 = 8.156603958 U = 8.156603958 Simplifying U = 8.156603958Subproblem 2
U + 1.5 = -9.656603958 Simplifying U + 1.5 = -9.656603958 Reorder the terms: 1.5 + U = -9.656603958 Solving 1.5 + U = -9.656603958 Solving for variable 'U'. Move all terms containing U to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + U = -9.656603958 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + U = -9.656603958 + -1.5 U = -9.656603958 + -1.5 Combine like terms: -9.656603958 + -1.5 = -11.156603958 U = -11.156603958 Simplifying U = -11.156603958Solution
The solution to the problem is based on the solutions from the subproblems. U = {8.156603958, -11.156603958}
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