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Simplifying z2 + -10z = -13 Reorder the terms: -10z + z2 = -13 Solving -10z + z2 = -13 Solving for variable 'z'. Reorder the terms: 13 + -10z + z2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -10z + -13 + z2 = 0 + -13 Reorder the terms: 13 + -13 + -10z + z2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -10z + z2 = 0 + -13 -10z + z2 = 0 + -13 Combine like terms: 0 + -13 = -13 -10z + z2 = -13 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 = -13 + 25 Reorder the terms: 25 + -10z + z2 = -13 + 25 Combine like terms: -13 + 25 = 12 25 + -10z + z2 = 12 Factor a perfect square on the left side: (z + -5)(z + -5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (z + -5) equal to 3.464101615 and -3.464101615.Subproblem 1
z + -5 = 3.464101615 Simplifying z + -5 = 3.464101615 Reorder the terms: -5 + z = 3.464101615 Solving -5 + z = 3.464101615 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 = 3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + z = 3.464101615 + 5 z = 3.464101615 + 5 Combine like terms: 3.464101615 + 5 = 8.464101615 z = 8.464101615 Simplifying z = 8.464101615Subproblem 2
z + -5 = -3.464101615 Simplifying z + -5 = -3.464101615 Reorder the terms: -5 + z = -3.464101615 Solving -5 + z = -3.464101615 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 = -3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + z = -3.464101615 + 5 z = -3.464101615 + 5 Combine like terms: -3.464101615 + 5 = 1.535898385 z = 1.535898385 Simplifying z = 1.535898385Solution
The solution to the problem is based on the solutions from the subproblems. z = {8.464101615, 1.535898385}
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