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Simplifying 4k(k + -3) + 7 = 2k + -1(k + 8) Reorder the terms: 4k(-3 + k) + 7 = 2k + -1(k + 8) (-3 * 4k + k * 4k) + 7 = 2k + -1(k + 8) (-12k + 4k2) + 7 = 2k + -1(k + 8) Reorder the terms: 7 + -12k + 4k2 = 2k + -1(k + 8) Reorder the terms: 7 + -12k + 4k2 = 2k + -1(8 + k) 7 + -12k + 4k2 = 2k + (8 * -1 + k * -1) 7 + -12k + 4k2 = 2k + (-8 + -1k) Reorder the terms: 7 + -12k + 4k2 = -8 + 2k + -1k Combine like terms: 2k + -1k = 1k 7 + -12k + 4k2 = -8 + 1k Solving 7 + -12k + 4k2 = -8 + 1k Solving for variable 'k'. Reorder the terms: 7 + 8 + -12k + -1k + 4k2 = -8 + 1k + 8 + -1k Combine like terms: 7 + 8 = 15 15 + -12k + -1k + 4k2 = -8 + 1k + 8 + -1k Combine like terms: -12k + -1k = -13k 15 + -13k + 4k2 = -8 + 1k + 8 + -1k Reorder the terms: 15 + -13k + 4k2 = -8 + 8 + 1k + -1k Combine like terms: -8 + 8 = 0 15 + -13k + 4k2 = 0 + 1k + -1k 15 + -13k + 4k2 = 1k + -1k Combine like terms: 1k + -1k = 0 15 + -13k + 4k2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -3.25k + k2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -3.25k + -3.75 + k2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -3.25k + k2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -3.25k + k2 = 0 + -3.75 -3.25k + k2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -3.25k + k2 = -3.75 The k term is -3.25k. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25k + 2.640625 + k2 = -3.75 + 2.640625 Reorder the terms: 2.640625 + -3.25k + k2 = -3.75 + 2.640625 Combine like terms: -3.75 + 2.640625 = -1.109375 2.640625 + -3.25k + k2 = -1.109375 Factor a perfect square on the left side: (k + -1.625)(k + -1.625) = -1.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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