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Simplifying -4(k + -8)(k + -8) = 16 Reorder the terms: -4(-8 + k)(k + -8) = 16 Reorder the terms: -4(-8 + k)(-8 + k) = 16 Multiply (-8 + k) * (-8 + k) -4(-8(-8 + k) + k(-8 + k)) = 16 -4((-8 * -8 + k * -8) + k(-8 + k)) = 16 -4((64 + -8k) + k(-8 + k)) = 16 -4(64 + -8k + (-8 * k + k * k)) = 16 -4(64 + -8k + (-8k + k2)) = 16 Combine like terms: -8k + -8k = -16k -4(64 + -16k + k2) = 16 (64 * -4 + -16k * -4 + k2 * -4) = 16 (-256 + 64k + -4k2) = 16 Solving -256 + 64k + -4k2 = 16 Solving for variable 'k'. Reorder the terms: -256 + -16 + 64k + -4k2 = 16 + -16 Combine like terms: -256 + -16 = -272 -272 + 64k + -4k2 = 16 + -16 Combine like terms: 16 + -16 = 0 -272 + 64k + -4k2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-68 + 16k + -1k2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-68 + 16k + -1k2)' equal to zero and attempt to solve: Simplifying -68 + 16k + -1k2 = 0 Solving -68 + 16k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 68 + -16k + k2 = 0 Move the constant term to the right: Add '-68' to each side of the equation. 68 + -16k + -68 + k2 = 0 + -68 Reorder the terms: 68 + -68 + -16k + k2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -16k + k2 = 0 + -68 -16k + k2 = 0 + -68 Combine like terms: 0 + -68 = -68 -16k + k2 = -68 The k term is -16k. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16k + 64 + k2 = -68 + 64 Reorder the terms: 64 + -16k + k2 = -68 + 64 Combine like terms: -68 + 64 = -4 64 + -16k + k2 = -4 Factor a perfect square on the left side: (k + -8)(k + -8) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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