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Simplifying z2 + -8z + -16 = 64 Reorder the terms: -16 + -8z + z2 = 64 Solving -16 + -8z + z2 = 64 Solving for variable 'z'. Reorder the terms: -16 + -64 + -8z + z2 = 64 + -64 Combine like terms: -16 + -64 = -80 -80 + -8z + z2 = 64 + -64 Combine like terms: 64 + -64 = 0 -80 + -8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -8z + 80 + z2 = 0 + 80 Reorder the terms: -80 + 80 + -8z + z2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -8z + z2 = 0 + 80 -8z + z2 = 0 + 80 Combine like terms: 0 + 80 = 80 -8z + z2 = 80 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 = 80 + 16 Reorder the terms: 16 + -8z + z2 = 80 + 16 Combine like terms: 80 + 16 = 96 16 + -8z + z2 = 96 Factor a perfect square on the left side: (z + -4)(z + -4) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (z + -4) equal to 9.797958971 and -9.797958971.Subproblem 1
z + -4 = 9.797958971 Simplifying z + -4 = 9.797958971 Reorder the terms: -4 + z = 9.797958971 Solving -4 + z = 9.797958971 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + z = 9.797958971 + 4 z = 9.797958971 + 4 Combine like terms: 9.797958971 + 4 = 13.797958971 z = 13.797958971 Simplifying z = 13.797958971Subproblem 2
z + -4 = -9.797958971 Simplifying z + -4 = -9.797958971 Reorder the terms: -4 + z = -9.797958971 Solving -4 + z = -9.797958971 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = -9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + z = -9.797958971 + 4 z = -9.797958971 + 4 Combine like terms: -9.797958971 + 4 = -5.797958971 z = -5.797958971 Simplifying z = -5.797958971Solution
The solution to the problem is based on the solutions from the subproblems. z = {13.797958971, -5.797958971}
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