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Simplifying 5z2 + -18z + 8 = 0 Reorder the terms: 8 + -18z + 5z2 = 0 Solving 8 + -18z + 5z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -3.6z + z2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -3.6z + -1.6 + z2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -3.6z + z2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -3.6z + z2 = 0 + -1.6 -3.6z + z2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -3.6z + z2 = -1.6 The z term is -3.6z. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6z + 3.24 + z2 = -1.6 + 3.24 Reorder the terms: 3.24 + -3.6z + z2 = -1.6 + 3.24 Combine like terms: -1.6 + 3.24 = 1.64 3.24 + -3.6z + z2 = 1.64 Factor a perfect square on the left side: (z + -1.8)(z + -1.8) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (z + -1.8) equal to 1.280624847 and -1.280624847.Subproblem 1
z + -1.8 = 1.280624847 Simplifying z + -1.8 = 1.280624847 Reorder the terms: -1.8 + z = 1.280624847 Solving -1.8 + z = 1.280624847 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + z = 1.280624847 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + z = 1.280624847 + 1.8 z = 1.280624847 + 1.8 Combine like terms: 1.280624847 + 1.8 = 3.080624847 z = 3.080624847 Simplifying z = 3.080624847Subproblem 2
z + -1.8 = -1.280624847 Simplifying z + -1.8 = -1.280624847 Reorder the terms: -1.8 + z = -1.280624847 Solving -1.8 + z = -1.280624847 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + z = -1.280624847 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + z = -1.280624847 + 1.8 z = -1.280624847 + 1.8 Combine like terms: -1.280624847 + 1.8 = 0.519375153 z = 0.519375153 Simplifying z = 0.519375153Solution
The solution to the problem is based on the solutions from the subproblems. z = {3.080624847, 0.519375153}
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