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Simplifying z2 + 10z = 1 Reorder the terms: 10z + z2 = 1 Solving 10z + z2 = 1 Solving for variable 'z'. Reorder the terms: -1 + 10z + z2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 10z + 1 + z2 = 0 + 1 Reorder the terms: -1 + 1 + 10z + z2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 10z + z2 = 0 + 1 10z + z2 = 0 + 1 Combine like terms: 0 + 1 = 1 10z + z2 = 1 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 = 1 + 25 Reorder the terms: 25 + 10z + z2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + 10z + z2 = 26 Factor a perfect square on the left side: (z + 5)(z + 5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (z + 5) equal to 5.099019514 and -5.099019514.Subproblem 1
z + 5 = 5.099019514 Simplifying z + 5 = 5.099019514 Reorder the terms: 5 + z = 5.099019514 Solving 5 + z = 5.099019514 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 = 5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + z = 5.099019514 + -5 z = 5.099019514 + -5 Combine like terms: 5.099019514 + -5 = 0.099019514 z = 0.099019514 Simplifying z = 0.099019514Subproblem 2
z + 5 = -5.099019514 Simplifying z + 5 = -5.099019514 Reorder the terms: 5 + z = -5.099019514 Solving 5 + z = -5.099019514 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 = -5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + z = -5.099019514 + -5 z = -5.099019514 + -5 Combine like terms: -5.099019514 + -5 = -10.099019514 z = -10.099019514 Simplifying z = -10.099019514Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.099019514, -10.099019514}
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