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Simplifying 10z2 + -8z + 1.6 = 0 Reorder the terms: 1.6 + -8z + 10z2 = 0 Solving 1.6 + -8z + 10z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.16 + -0.8z + z2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -0.8z + -0.16 + z2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -0.8z + z2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -0.8z + z2 = 0 + -0.16 -0.8z + z2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -0.8z + z2 = -0.16 The z term is -0.8z. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8z + 0.16 + z2 = -0.16 + 0.16 Reorder the terms: 0.16 + -0.8z + z2 = -0.16 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.16 + -0.8z + z2 = 0.00 Factor a perfect square on the left side: (z + -0.4)(z + -0.4) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (z + -0.4) equal to 0.00 and 0.00.Subproblem 1
z + -0.4 = 0.00 Simplifying z + -0.4 = 0.00 Reorder the terms: -0.4 + z = 0.00 Solving -0.4 + z = 0.00 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + z = 0.00 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + z = 0.00 + 0.4 z = 0.00 + 0.4 Combine like terms: 0.00 + 0.4 = 0.4 z = 0.4 Simplifying z = 0.4Subproblem 2
z + -0.4 = 0.00 Simplifying z + -0.4 = 0.00 Reorder the terms: -0.4 + z = 0.00 Solving -0.4 + z = 0.00 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + z = 0.00 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + z = 0.00 + 0.4 z = 0.00 + 0.4 Combine like terms: 0.00 + 0.4 = 0.4 z = 0.4 Simplifying z = 0.4Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.4, 0.4}
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