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Simplifying z2 + -8z = 21 Reorder the terms: -8z + z2 = 21 Solving -8z + z2 = 21 Solving for variable 'z'. Reorder the terms: -21 + -8z + z2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -8z + 21 + z2 = 0 + 21 Reorder the terms: -21 + 21 + -8z + z2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -8z + z2 = 0 + 21 -8z + z2 = 0 + 21 Combine like terms: 0 + 21 = 21 -8z + z2 = 21 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 = 21 + 16 Reorder the terms: 16 + -8z + z2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + -8z + z2 = 37 Factor a perfect square on the left side: (z + -4)(z + -4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (z + -4) equal to 6.08276253 and -6.08276253.Subproblem 1
z + -4 = 6.08276253 Simplifying z + -4 = 6.08276253 Reorder the terms: -4 + z = 6.08276253 Solving -4 + z = 6.08276253 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 = 6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + z = 6.08276253 + 4 z = 6.08276253 + 4 Combine like terms: 6.08276253 + 4 = 10.08276253 z = 10.08276253 Simplifying z = 10.08276253Subproblem 2
z + -4 = -6.08276253 Simplifying z + -4 = -6.08276253 Reorder the terms: -4 + z = -6.08276253 Solving -4 + z = -6.08276253 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 = -6.08276253 + 4 Combine like terms: -4 + 4 = 0 0 + z = -6.08276253 + 4 z = -6.08276253 + 4 Combine like terms: -6.08276253 + 4 = -2.08276253 z = -2.08276253 Simplifying z = -2.08276253Solution
The solution to the problem is based on the solutions from the subproblems. z = {10.08276253, -2.08276253}
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