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Simplifying 0.5z2 + 7(2) = z + -5(z) Multiply 7 * 2 0.5z2 + 14 = z + -5(z) Reorder the terms: 14 + 0.5z2 = z + -5(z) Combine like terms: z + -5z = -4z 14 + 0.5z2 = -4z Solving 14 + 0.5z2 = -4z Solving for variable 'z'. Reorder the terms: 14 + 4z + 0.5z2 = -4z + 4z Combine like terms: -4z + 4z = 0 14 + 4z + 0.5z2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 28 + 8z + z2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + 8z + -28 + z2 = 0 + -28 Reorder the terms: 28 + -28 + 8z + z2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 8z + z2 = 0 + -28 8z + z2 = 0 + -28 Combine like terms: 0 + -28 = -28 8z + z2 = -28 The z term is 8z. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8z + 16 + z2 = -28 + 16 Reorder the terms: 16 + 8z + z2 = -28 + 16 Combine like terms: -28 + 16 = -12 16 + 8z + z2 = -12 Factor a perfect square on the left side: (z + 4)(z + 4) = -12 Can't calculate square root of the right side. The solution to this equation could not be determined.
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