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Simplifying z2 + -10z = 20 Reorder the terms: -10z + z2 = 20 Solving -10z + z2 = 20 Solving for variable 'z'. Reorder the terms: -20 + -10z + z2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -10z + 20 + z2 = 0 + 20 Reorder the terms: -20 + 20 + -10z + z2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -10z + z2 = 0 + 20 -10z + z2 = 0 + 20 Combine like terms: 0 + 20 = 20 -10z + z2 = 20 The z term is -10z. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10z + 25 + z2 = 20 + 25 Reorder the terms: 25 + -10z + z2 = 20 + 25 Combine like terms: 20 + 25 = 45 25 + -10z + z2 = 45 Factor a perfect square on the left side: (z + -5)(z + -5) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (z + -5) equal to 6.708203933 and -6.708203933.Subproblem 1
z + -5 = 6.708203933 Simplifying z + -5 = 6.708203933 Reorder the terms: -5 + z = 6.708203933 Solving -5 + z = 6.708203933 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 6.708203933 + 5 Combine like terms: -5 + 5 = 0 0 + z = 6.708203933 + 5 z = 6.708203933 + 5 Combine like terms: 6.708203933 + 5 = 11.708203933 z = 11.708203933 Simplifying z = 11.708203933Subproblem 2
z + -5 = -6.708203933 Simplifying z + -5 = -6.708203933 Reorder the terms: -5 + z = -6.708203933 Solving -5 + z = -6.708203933 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -6.708203933 + 5 Combine like terms: -5 + 5 = 0 0 + z = -6.708203933 + 5 z = -6.708203933 + 5 Combine like terms: -6.708203933 + 5 = -1.708203933 z = -1.708203933 Simplifying z = -1.708203933Solution
The solution to the problem is based on the solutions from the subproblems. z = {11.708203933, -1.708203933}
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