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Simplifying z2 + z = 5 Reorder the terms: z + z2 = 5 Solving z + z2 = 5 Solving for variable 'z'. Reorder the terms: -5 + z + z2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + z + 5 + z2 = 0 + 5 Reorder the terms: -5 + 5 + z + z2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + z + z2 = 0 + 5 z + z2 = 0 + 5 Combine like terms: 0 + 5 = 5 z + z2 = 5 The z term is z. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. z + 0.25 + z2 = 5 + 0.25 Reorder the terms: 0.25 + z + z2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + z + z2 = 5.25 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (z + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
z + 0.5 = 2.291287847 Simplifying z + 0.5 = 2.291287847 Reorder the terms: 0.5 + z = 2.291287847 Solving 0.5 + z = 2.291287847 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 2.291287847 + -0.5 z = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 z = 1.791287847 Simplifying z = 1.791287847Subproblem 2
z + 0.5 = -2.291287847 Simplifying z + 0.5 = -2.291287847 Reorder the terms: 0.5 + z = -2.291287847 Solving 0.5 + z = -2.291287847 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -2.291287847 + -0.5 z = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 z = -2.791287847 Simplifying z = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.791287847, -2.791287847}
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