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Simplifying 2u2 + 4u + 43 = (u + 6)(u + 6) Reorder the terms: 43 + 4u + 2u2 = (u + 6)(u + 6) Reorder the terms: 43 + 4u + 2u2 = (6 + u)(u + 6) Reorder the terms: 43 + 4u + 2u2 = (6 + u)(6 + u) Multiply (6 + u) * (6 + u) 43 + 4u + 2u2 = (6(6 + u) + u(6 + u)) 43 + 4u + 2u2 = ((6 * 6 + u * 6) + u(6 + u)) 43 + 4u + 2u2 = ((36 + 6u) + u(6 + u)) 43 + 4u + 2u2 = (36 + 6u + (6 * u + u * u)) 43 + 4u + 2u2 = (36 + 6u + (6u + u2)) Combine like terms: 6u + 6u = 12u 43 + 4u + 2u2 = (36 + 12u + u2) Solving 43 + 4u + 2u2 = 36 + 12u + u2 Solving for variable 'u'. Reorder the terms: 43 + -36 + 4u + -12u + 2u2 + -1u2 = 36 + 12u + u2 + -36 + -12u + -1u2 Combine like terms: 43 + -36 = 7 7 + 4u + -12u + 2u2 + -1u2 = 36 + 12u + u2 + -36 + -12u + -1u2 Combine like terms: 4u + -12u = -8u 7 + -8u + 2u2 + -1u2 = 36 + 12u + u2 + -36 + -12u + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 7 + -8u + 1u2 = 36 + 12u + u2 + -36 + -12u + -1u2 Reorder the terms: 7 + -8u + 1u2 = 36 + -36 + 12u + -12u + u2 + -1u2 Combine like terms: 36 + -36 = 0 7 + -8u + 1u2 = 0 + 12u + -12u + u2 + -1u2 7 + -8u + 1u2 = 12u + -12u + u2 + -1u2 Combine like terms: 12u + -12u = 0 7 + -8u + 1u2 = 0 + u2 + -1u2 7 + -8u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 7 + -8u + 1u2 = 0 Factor a trinomial. (1 + -1u)(7 + -1u) = 0Subproblem 1
Set the factor '(1 + -1u)' equal to zero and attempt to solve: Simplifying 1 + -1u = 0 Solving 1 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1u = 0 + -1 -1u = 0 + -1 Combine like terms: 0 + -1 = -1 -1u = -1 Divide each side by '-1'. u = 1 Simplifying u = 1Subproblem 2
Set the factor '(7 + -1u)' equal to zero and attempt to solve: Simplifying 7 + -1u = 0 Solving 7 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1u = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1u = 0 + -7 -1u = 0 + -7 Combine like terms: 0 + -7 = -7 -1u = -7 Divide each side by '-1'. u = 7 Simplifying u = 7Solution
u = {1, 7}
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