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Simplifying z2 + 10z + 25 = 47 Reorder the terms: 25 + 10z + z2 = 47 Solving 25 + 10z + z2 = 47 Solving for variable 'z'. Reorder the terms: 25 + -47 + 10z + z2 = 47 + -47 Combine like terms: 25 + -47 = -22 -22 + 10z + z2 = 47 + -47 Combine like terms: 47 + -47 = 0 -22 + 10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 10z + 22 + z2 = 0 + 22 Reorder the terms: -22 + 22 + 10z + z2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 10z + z2 = 0 + 22 10z + z2 = 0 + 22 Combine like terms: 0 + 22 = 22 10z + z2 = 22 The z term is 10z. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10z + 25 + z2 = 22 + 25 Reorder the terms: 25 + 10z + z2 = 22 + 25 Combine like terms: 22 + 25 = 47 25 + 10z + z2 = 47 Factor a perfect square on the left side: (z + 5)(z + 5) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (z + 5) equal to 6.8556546 and -6.8556546.Subproblem 1
z + 5 = 6.8556546 Simplifying z + 5 = 6.8556546 Reorder the terms: 5 + z = 6.8556546 Solving 5 + z = 6.8556546 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 6.8556546 + -5 Combine like terms: 5 + -5 = 0 0 + z = 6.8556546 + -5 z = 6.8556546 + -5 Combine like terms: 6.8556546 + -5 = 1.8556546 z = 1.8556546 Simplifying z = 1.8556546Subproblem 2
z + 5 = -6.8556546 Simplifying z + 5 = -6.8556546 Reorder the terms: 5 + z = -6.8556546 Solving 5 + z = -6.8556546 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = -6.8556546 + -5 Combine like terms: 5 + -5 = 0 0 + z = -6.8556546 + -5 z = -6.8556546 + -5 Combine like terms: -6.8556546 + -5 = -11.8556546 z = -11.8556546 Simplifying z = -11.8556546Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.8556546, -11.8556546}
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