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Simplifying 4z + -2 = z2 Reorder the terms: -2 + 4z = z2 Solving -2 + 4z = z2 Solving for variable 'z'. Combine like terms: z2 + -1z2 = 0 -2 + 4z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -4z + z2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + -4z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4z + z2 = 0 + -2 -4z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4z + z2 = -2 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 = -2 + 4 Reorder the terms: 4 + -4z + z2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4z + z2 = 2 Factor a perfect square on the left side: (z + -2)(z + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (z + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
z + -2 = 1.414213562 Simplifying z + -2 = 1.414213562 Reorder the terms: -2 + z = 1.414213562 Solving -2 + z = 1.414213562 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 = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + z = 1.414213562 + 2 z = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 z = 3.414213562 Simplifying z = 3.414213562Subproblem 2
z + -2 = -1.414213562 Simplifying z + -2 = -1.414213562 Reorder the terms: -2 + z = -1.414213562 Solving -2 + z = -1.414213562 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 = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + z = -1.414213562 + 2 z = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 z = 0.585786438 Simplifying z = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. z = {3.414213562, 0.585786438}
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