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Simplifying (x + -1)(x + 1) = x2 + kx + m Reorder the terms: (-1 + x)(x + 1) = x2 + kx + m Reorder the terms: (-1 + x)(1 + x) = x2 + kx + m Multiply (-1 + x) * (1 + x) (-1(1 + x) + x(1 + x)) = x2 + kx + m ((1 * -1 + x * -1) + x(1 + x)) = x2 + kx + m ((-1 + -1x) + x(1 + x)) = x2 + kx + m (-1 + -1x + (1 * x + x * x)) = x2 + kx + m (-1 + -1x + (1x + x2)) = x2 + kx + m Combine like terms: -1x + 1x = 0 (-1 + 0 + x2) = x2 + kx + m (-1 + x2) = x2 + kx + m Reorder the terms: -1 + x2 = kx + m + x2 Add '-1x2' to each side of the equation. -1 + x2 + -1x2 = kx + m + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + 0 = kx + m + x2 + -1x2 -1 = kx + m + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 = kx + m + 0 -1 = kx + m Solving -1 = kx + m Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1kx' to each side of the equation. -1 + -1kx = kx + -1kx + m Combine like terms: kx + -1kx = 0 -1 + -1kx = 0 + m -1 + -1kx = m Add '1' to each side of the equation. -1 + 1 + -1kx = 1 + m Combine like terms: -1 + 1 = 0 0 + -1kx = 1 + m -1kx = 1 + m Divide each side by '-1x'. k = -1x-1 + -1mx-1 Simplifying k = -1x-1 + -1mx-1 Reorder the terms: k = -1mx-1 + -1x-1
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