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Simplifying z2 + 4z + -4 = 0 Reorder the terms: -4 + 4z + z2 = 0 Solving -4 + 4z + 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 + 4z + 4 + z2 = 0 + 4 Reorder the terms: -4 + 4 + 4z + z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4z + z2 = 0 + 4 4z + z2 = 0 + 4 Combine like terms: 0 + 4 = 4 4z + z2 = 4 The z term is 4z. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z + 4 + z2 = 4 + 4 Reorder the terms: 4 + 4z + z2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4z + z2 = 8 Factor a perfect square on the left side: (z + 2)(z + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (z + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
z + 2 = 2.828427125 Simplifying z + 2 = 2.828427125 Reorder the terms: 2 + z = 2.828427125 Solving 2 + z = 2.828427125 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + z = 2.828427125 + -2 z = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 z = 0.828427125 Simplifying z = 0.828427125Subproblem 2
z + 2 = -2.828427125 Simplifying z + 2 = -2.828427125 Reorder the terms: 2 + z = -2.828427125 Solving 2 + z = -2.828427125 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + z = -2.828427125 + -2 z = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 z = -4.828427125 Simplifying z = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.828427125, -4.828427125}
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