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Simplifying 4k2 + 4k + 1 = 17(4k2 + 4k + 1) Reorder the terms: 1 + 4k + 4k2 = 17(4k2 + 4k + 1) Reorder the terms: 1 + 4k + 4k2 = 17(1 + 4k + 4k2) 1 + 4k + 4k2 = (1 * 17 + 4k * 17 + 4k2 * 17) 1 + 4k + 4k2 = (17 + 68k + 68k2) Solving 1 + 4k + 4k2 = 17 + 68k + 68k2 Solving for variable 'k'. Reorder the terms: 1 + -17 + 4k + -68k + 4k2 + -68k2 = 17 + 68k + 68k2 + -17 + -68k + -68k2 Combine like terms: 1 + -17 = -16 -16 + 4k + -68k + 4k2 + -68k2 = 17 + 68k + 68k2 + -17 + -68k + -68k2 Combine like terms: 4k + -68k = -64k -16 + -64k + 4k2 + -68k2 = 17 + 68k + 68k2 + -17 + -68k + -68k2 Combine like terms: 4k2 + -68k2 = -64k2 -16 + -64k + -64k2 = 17 + 68k + 68k2 + -17 + -68k + -68k2 Reorder the terms: -16 + -64k + -64k2 = 17 + -17 + 68k + -68k + 68k2 + -68k2 Combine like terms: 17 + -17 = 0 -16 + -64k + -64k2 = 0 + 68k + -68k + 68k2 + -68k2 -16 + -64k + -64k2 = 68k + -68k + 68k2 + -68k2 Combine like terms: 68k + -68k = 0 -16 + -64k + -64k2 = 0 + 68k2 + -68k2 -16 + -64k + -64k2 = 68k2 + -68k2 Combine like terms: 68k2 + -68k2 = 0 -16 + -64k + -64k2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(1 + 4k + 4k2) = 0 Factor a trinomial. -16((1 + 2k)(1 + 2k)) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(1 + 2k)' equal to zero and attempt to solve: Simplifying 1 + 2k = 0 Solving 1 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2k = 0 + -1 2k = 0 + -1 Combine like terms: 0 + -1 = -1 2k = -1 Divide each side by '2'. k = -0.5 Simplifying k = -0.5Subproblem 2
Set the factor '(1 + 2k)' equal to zero and attempt to solve: Simplifying 1 + 2k = 0 Solving 1 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2k = 0 + -1 2k = 0 + -1 Combine like terms: 0 + -1 = -1 2k = -1 Divide each side by '2'. k = -0.5 Simplifying k = -0.5Solution
k = {-0.5, -0.5}
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