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Simplifying sqrt(-7 + -2k) = sqrt(3k + 28) (-7 * qrst + -2k * qrst) = sqrt(3k + 28) Reorder the terms: (-2kqrst + -7qrst) = sqrt(3k + 28) (-2kqrst + -7qrst) = sqrt(3k + 28) Reorder the terms: -2kqrst + -7qrst = qrst(28 + 3k) -2kqrst + -7qrst = (28 * qrst + 3k * qrst) Reorder the terms: -2kqrst + -7qrst = (3kqrst + 28qrst) -2kqrst + -7qrst = (3kqrst + 28qrst) Solving -2kqrst + -7qrst = 3kqrst + 28qrst Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3kqrst' to each side of the equation. -2kqrst + -3kqrst + -7qrst = 3kqrst + -3kqrst + 28qrst Combine like terms: -2kqrst + -3kqrst = -5kqrst -5kqrst + -7qrst = 3kqrst + -3kqrst + 28qrst Combine like terms: 3kqrst + -3kqrst = 0 -5kqrst + -7qrst = 0 + 28qrst -5kqrst + -7qrst = 28qrst Add '7qrst' to each side of the equation. -5kqrst + -7qrst + 7qrst = 28qrst + 7qrst Combine like terms: -7qrst + 7qrst = 0 -5kqrst + 0 = 28qrst + 7qrst -5kqrst = 28qrst + 7qrst Combine like terms: 28qrst + 7qrst = 35qrst -5kqrst = 35qrst Divide each side by '-5qrst'. k = -7 Simplifying k = -7
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