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Simplifying z2 + -8z = -3 Reorder the terms: -8z + z2 = -3 Solving -8z + z2 = -3 Solving for variable 'z'. Reorder the terms: 3 + -8z + z2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8z + -3 + z2 = 0 + -3 Reorder the terms: 3 + -3 + -8z + z2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8z + z2 = 0 + -3 -8z + z2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8z + z2 = -3 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 = -3 + 16 Reorder the terms: 16 + -8z + z2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8z + z2 = 13 Factor a perfect square on the left side: (z + -4)(z + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (z + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
z + -4 = 3.605551275 Simplifying z + -4 = 3.605551275 Reorder the terms: -4 + z = 3.605551275 Solving -4 + z = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + z = 3.605551275 + 4 z = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 z = 7.605551275 Simplifying z = 7.605551275Subproblem 2
z + -4 = -3.605551275 Simplifying z + -4 = -3.605551275 Reorder the terms: -4 + z = -3.605551275 Solving -4 + z = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + z = -3.605551275 + 4 z = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 z = 0.394448725 Simplifying z = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.605551275, 0.394448725}
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