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Simplifying z2 + 9z = -10 Reorder the terms: 9z + z2 = -10 Solving 9z + z2 = -10 Solving for variable 'z'. Reorder the terms: 10 + 9z + z2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + 9z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 9z + -10 + z2 = 0 + -10 Reorder the terms: 10 + -10 + 9z + z2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 9z + z2 = 0 + -10 9z + z2 = 0 + -10 Combine like terms: 0 + -10 = -10 9z + z2 = -10 The z term is 9z. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9z + 20.25 + z2 = -10 + 20.25 Reorder the terms: 20.25 + 9z + z2 = -10 + 20.25 Combine like terms: -10 + 20.25 = 10.25 20.25 + 9z + z2 = 10.25 Factor a perfect square on the left side: (z + 4.5)(z + 4.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (z + 4.5) equal to 3.201562119 and -3.201562119.Subproblem 1
z + 4.5 = 3.201562119 Simplifying z + 4.5 = 3.201562119 Reorder the terms: 4.5 + z = 3.201562119 Solving 4.5 + z = 3.201562119 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = 3.201562119 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = 3.201562119 + -4.5 z = 3.201562119 + -4.5 Combine like terms: 3.201562119 + -4.5 = -1.298437881 z = -1.298437881 Simplifying z = -1.298437881Subproblem 2
z + 4.5 = -3.201562119 Simplifying z + 4.5 = -3.201562119 Reorder the terms: 4.5 + z = -3.201562119 Solving 4.5 + z = -3.201562119 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = -3.201562119 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = -3.201562119 + -4.5 z = -3.201562119 + -4.5 Combine like terms: -3.201562119 + -4.5 = -7.701562119 z = -7.701562119 Simplifying z = -7.701562119Solution
The solution to the problem is based on the solutions from the subproblems. z = {-1.298437881, -7.701562119}
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