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Simplifying z + -1z2 = 0.25 Solving z + -1z2 = 0.25 Solving for variable 'z'. Reorder the terms: -0.25 + z + -1z2 = 0.25 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 -0.25 + z + -1z2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.25 + -1z + z2 = 0.00 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1z + -0.25 + z2 = 0.00 + -0.25 Reorder the terms: 0.25 + -0.25 + -1z + z2 = 0.00 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1z + z2 = 0.00 + -0.25 -1z + z2 = 0.00 + -0.25 Combine like terms: 0.00 + -0.25 = -0.25 -1z + z2 = -0.25 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. -1z + 0.25 + z2 = -0.25 + 0.25 Reorder the terms: 0.25 + -1z + z2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -1z + z2 = 0.00 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (z + 0.5) equal to 0.00 and 0.00.Subproblem 1
z + 0.5 = 0.00 Simplifying z + 0.5 = 0.00 Reorder the terms: 0.5 + z = 0.00 Solving 0.5 + z = 0.00 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 = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 0.00 + -0.5 z = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 z = -0.5 Simplifying z = -0.5Subproblem 2
z + 0.5 = 0.00 Simplifying z + 0.5 = 0.00 Reorder the terms: 0.5 + z = 0.00 Solving 0.5 + z = 0.00 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 = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 0.00 + -0.5 z = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 z = -0.5 Simplifying z = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.5, -0.5}
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