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Simplifying 2u2 + 13u + 10 = (u + 4)(u + 4) Reorder the terms: 10 + 13u + 2u2 = (u + 4)(u + 4) Reorder the terms: 10 + 13u + 2u2 = (4 + u)(u + 4) Reorder the terms: 10 + 13u + 2u2 = (4 + u)(4 + u) Multiply (4 + u) * (4 + u) 10 + 13u + 2u2 = (4(4 + u) + u(4 + u)) 10 + 13u + 2u2 = ((4 * 4 + u * 4) + u(4 + u)) 10 + 13u + 2u2 = ((16 + 4u) + u(4 + u)) 10 + 13u + 2u2 = (16 + 4u + (4 * u + u * u)) 10 + 13u + 2u2 = (16 + 4u + (4u + u2)) Combine like terms: 4u + 4u = 8u 10 + 13u + 2u2 = (16 + 8u + u2) Solving 10 + 13u + 2u2 = 16 + 8u + u2 Solving for variable 'u'. Reorder the terms: 10 + -16 + 13u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Combine like terms: 10 + -16 = -6 -6 + 13u + -8u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Combine like terms: 13u + -8u = 5u -6 + 5u + 2u2 + -1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Combine like terms: 2u2 + -1u2 = 1u2 -6 + 5u + 1u2 = 16 + 8u + u2 + -16 + -8u + -1u2 Reorder the terms: -6 + 5u + 1u2 = 16 + -16 + 8u + -8u + u2 + -1u2 Combine like terms: 16 + -16 = 0 -6 + 5u + 1u2 = 0 + 8u + -8u + u2 + -1u2 -6 + 5u + 1u2 = 8u + -8u + u2 + -1u2 Combine like terms: 8u + -8u = 0 -6 + 5u + 1u2 = 0 + u2 + -1u2 -6 + 5u + 1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 -6 + 5u + 1u2 = 0 Factor a trinomial. (-6 + -1u)(1 + -1u) = 0Subproblem 1
Set the factor '(-6 + -1u)' equal to zero and attempt to solve: Simplifying -6 + -1u = 0 Solving -6 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1u = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1u = 0 + 6 -1u = 0 + 6 Combine like terms: 0 + 6 = 6 -1u = 6 Divide each side by '-1'. u = -6 Simplifying u = -6Subproblem 2
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 = 1Solution
u = {-6, 1}
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