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Simplifying z2 + 5z + -4 = 0 Reorder the terms: -4 + 5z + z2 = 0 Solving -4 + 5z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5z + 4 + z2 = 0 + 4 Reorder the terms: -4 + 4 + 5z + z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5z + z2 = 0 + 4 5z + z2 = 0 + 4 Combine like terms: 0 + 4 = 4 5z + z2 = 4 The z term is 5z. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5z + 6.25 + z2 = 4 + 6.25 Reorder the terms: 6.25 + 5z + z2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5z + z2 = 10.25 Factor a perfect square on the left side: (z + 2.5)(z + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (z + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
z + 2.5 = 3.201562119 Simplifying z + 2.5 = 3.201562119 Reorder the terms: 2.5 + z = 3.201562119 Solving 2.5 + z = 3.201562119 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = 3.201562119 + -2.5 z = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 z = 0.701562119 Simplifying z = 0.701562119Subproblem 2
z + 2.5 = -3.201562119 Simplifying z + 2.5 = -3.201562119 Reorder the terms: 2.5 + z = -3.201562119 Solving 2.5 + z = -3.201562119 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = -3.201562119 + -2.5 z = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 z = -5.701562119 Simplifying z = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.701562119, -5.701562119}
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