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Simplifying 2 = 16z2 + z Reorder the terms: 2 = z + 16z2 Solving 2 = z + 16z2 Solving for variable 'z'. Reorder the terms: 2 + -1z + -16z2 = z + -1z + 16z2 + -16z2 Combine like terms: z + -1z = 0 2 + -1z + -16z2 = 0 + 16z2 + -16z2 2 + -1z + -16z2 = 16z2 + -16z2 Combine like terms: 16z2 + -16z2 = 0 2 + -1z + -16z2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.125 + 0.0625z + z2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.0625z + 0.125 + z2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.0625z + z2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.0625z + z2 = 0 + 0.125 0.0625z + z2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.0625z + z2 = 0.125 The z term is 0.0625z. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625z + 0.0009765625 + z2 = 0.125 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625z + z2 = 0.125 + 0.0009765625 Combine like terms: 0.125 + 0.0009765625 = 0.1259765625 0.0009765625 + 0.0625z + z2 = 0.1259765625 Factor a perfect square on the left side: (z + 0.03125)(z + 0.03125) = 0.1259765625 Calculate the square root of the right side: 0.354931772 Break this problem into two subproblems by setting (z + 0.03125) equal to 0.354931772 and -0.354931772.Subproblem 1
z + 0.03125 = 0.354931772 Simplifying z + 0.03125 = 0.354931772 Reorder the terms: 0.03125 + z = 0.354931772 Solving 0.03125 + z = 0.354931772 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + z = 0.354931772 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + z = 0.354931772 + -0.03125 z = 0.354931772 + -0.03125 Combine like terms: 0.354931772 + -0.03125 = 0.323681772 z = 0.323681772 Simplifying z = 0.323681772Subproblem 2
z + 0.03125 = -0.354931772 Simplifying z + 0.03125 = -0.354931772 Reorder the terms: 0.03125 + z = -0.354931772 Solving 0.03125 + z = -0.354931772 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + z = -0.354931772 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + z = -0.354931772 + -0.03125 z = -0.354931772 + -0.03125 Combine like terms: -0.354931772 + -0.03125 = -0.386181772 z = -0.386181772 Simplifying z = -0.386181772Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.323681772, -0.386181772}
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