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Simplifying z2 + -10z = -19 Reorder the terms: -10z + z2 = -19 Solving -10z + z2 = -19 Solving for variable 'z'. Reorder the terms: 19 + -10z + z2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + -10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -10z + -19 + z2 = 0 + -19 Reorder the terms: 19 + -19 + -10z + z2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -10z + z2 = 0 + -19 -10z + z2 = 0 + -19 Combine like terms: 0 + -19 = -19 -10z + z2 = -19 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 = -19 + 25 Reorder the terms: 25 + -10z + z2 = -19 + 25 Combine like terms: -19 + 25 = 6 25 + -10z + z2 = 6 Factor a perfect square on the left side: (z + -5)(z + -5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (z + -5) equal to 2.449489743 and -2.449489743.Subproblem 1
z + -5 = 2.449489743 Simplifying z + -5 = 2.449489743 Reorder the terms: -5 + z = 2.449489743 Solving -5 + z = 2.449489743 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 = 2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + z = 2.449489743 + 5 z = 2.449489743 + 5 Combine like terms: 2.449489743 + 5 = 7.449489743 z = 7.449489743 Simplifying z = 7.449489743Subproblem 2
z + -5 = -2.449489743 Simplifying z + -5 = -2.449489743 Reorder the terms: -5 + z = -2.449489743 Solving -5 + z = -2.449489743 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 = -2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + z = -2.449489743 + 5 z = -2.449489743 + 5 Combine like terms: -2.449489743 + 5 = 2.550510257 z = 2.550510257 Simplifying z = 2.550510257Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.449489743, 2.550510257}
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