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Simplifying z2 + -25z = -48 Reorder the terms: -25z + z2 = -48 Solving -25z + z2 = -48 Solving for variable 'z'. Reorder the terms: 48 + -25z + z2 = -48 + 48 Combine like terms: -48 + 48 = 0 48 + -25z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -25z + -48 + z2 = 0 + -48 Reorder the terms: 48 + -48 + -25z + z2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -25z + z2 = 0 + -48 -25z + z2 = 0 + -48 Combine like terms: 0 + -48 = -48 -25z + z2 = -48 The z term is -25z. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25z + 156.25 + z2 = -48 + 156.25 Reorder the terms: 156.25 + -25z + z2 = -48 + 156.25 Combine like terms: -48 + 156.25 = 108.25 156.25 + -25z + z2 = 108.25 Factor a perfect square on the left side: (z + -12.5)(z + -12.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (z + -12.5) equal to 10.404326023 and -10.404326023.Subproblem 1
z + -12.5 = 10.404326023 Simplifying z + -12.5 = 10.404326023 Reorder the terms: -12.5 + z = 10.404326023 Solving -12.5 + z = 10.404326023 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + z = 10.404326023 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + z = 10.404326023 + 12.5 z = 10.404326023 + 12.5 Combine like terms: 10.404326023 + 12.5 = 22.904326023 z = 22.904326023 Simplifying z = 22.904326023Subproblem 2
z + -12.5 = -10.404326023 Simplifying z + -12.5 = -10.404326023 Reorder the terms: -12.5 + z = -10.404326023 Solving -12.5 + z = -10.404326023 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + z = -10.404326023 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + z = -10.404326023 + 12.5 z = -10.404326023 + 12.5 Combine like terms: -10.404326023 + 12.5 = 2.095673977 z = 2.095673977 Simplifying z = 2.095673977Solution
The solution to the problem is based on the solutions from the subproblems. z = {22.904326023, 2.095673977}
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