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Simplifying z2 + -1z + -50 = 0 Reorder the terms: -50 + -1z + z2 = 0 Solving -50 + -1z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -1z + 50 + z2 = 0 + 50 Reorder the terms: -50 + 50 + -1z + z2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -1z + z2 = 0 + 50 -1z + z2 = 0 + 50 Combine like terms: 0 + 50 = 50 -1z + z2 = 50 The z term is -1z. 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 = 50 + 0.25 Reorder the terms: 0.25 + -1z + z2 = 50 + 0.25 Combine like terms: 50 + 0.25 = 50.25 0.25 + -1z + z2 = 50.25 Factor a perfect square on the left side: (z + -0.5)(z + -0.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (z + -0.5) equal to 7.088723439 and -7.088723439.Subproblem 1
z + -0.5 = 7.088723439 Simplifying z + -0.5 = 7.088723439 Reorder the terms: -0.5 + z = 7.088723439 Solving -0.5 + z = 7.088723439 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 = 7.088723439 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 7.088723439 + 0.5 z = 7.088723439 + 0.5 Combine like terms: 7.088723439 + 0.5 = 7.588723439 z = 7.588723439 Simplifying z = 7.588723439Subproblem 2
z + -0.5 = -7.088723439 Simplifying z + -0.5 = -7.088723439 Reorder the terms: -0.5 + z = -7.088723439 Solving -0.5 + z = -7.088723439 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 = -7.088723439 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -7.088723439 + 0.5 z = -7.088723439 + 0.5 Combine like terms: -7.088723439 + 0.5 = -6.588723439 z = -6.588723439 Simplifying z = -6.588723439Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.588723439, -6.588723439}
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