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Simplifying 729 = z(z + -16) Reorder the terms: 729 = z(-16 + z) 729 = (-16 * z + z * z) 729 = (-16z + z2) Solving 729 = -16z + z2 Solving for variable 'z'. Reorder the terms: 729 + 16z + -1z2 = -16z + 16z + z2 + -1z2 Combine like terms: -16z + 16z = 0 729 + 16z + -1z2 = 0 + z2 + -1z2 729 + 16z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 729 + 16z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -729 + -16z + z2 = 0 Move the constant term to the right: Add '729' to each side of the equation. -729 + -16z + 729 + z2 = 0 + 729 Reorder the terms: -729 + 729 + -16z + z2 = 0 + 729 Combine like terms: -729 + 729 = 0 0 + -16z + z2 = 0 + 729 -16z + z2 = 0 + 729 Combine like terms: 0 + 729 = 729 -16z + z2 = 729 The z term is -16z. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16z + 64 + z2 = 729 + 64 Reorder the terms: 64 + -16z + z2 = 729 + 64 Combine like terms: 729 + 64 = 793 64 + -16z + z2 = 793 Factor a perfect square on the left side: (z + -8)(z + -8) = 793 Calculate the square root of the right side: 28.160255681 Break this problem into two subproblems by setting (z + -8) equal to 28.160255681 and -28.160255681.Subproblem 1
z + -8 = 28.160255681 Simplifying z + -8 = 28.160255681 Reorder the terms: -8 + z = 28.160255681 Solving -8 + z = 28.160255681 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = 28.160255681 + 8 Combine like terms: -8 + 8 = 0 0 + z = 28.160255681 + 8 z = 28.160255681 + 8 Combine like terms: 28.160255681 + 8 = 36.160255681 z = 36.160255681 Simplifying z = 36.160255681Subproblem 2
z + -8 = -28.160255681 Simplifying z + -8 = -28.160255681 Reorder the terms: -8 + z = -28.160255681 Solving -8 + z = -28.160255681 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = -28.160255681 + 8 Combine like terms: -8 + 8 = 0 0 + z = -28.160255681 + 8 z = -28.160255681 + 8 Combine like terms: -28.160255681 + 8 = -20.160255681 z = -20.160255681 Simplifying z = -20.160255681Solution
The solution to the problem is based on the solutions from the subproblems. z = {36.160255681, -20.160255681}
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