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Simplifying z2 + 7z = 7 Reorder the terms: 7z + z2 = 7 Solving 7z + z2 = 7 Solving for variable 'z'. Reorder the terms: -7 + 7z + z2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 7z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 7z + 7 + z2 = 0 + 7 Reorder the terms: -7 + 7 + 7z + z2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 7z + z2 = 0 + 7 7z + z2 = 0 + 7 Combine like terms: 0 + 7 = 7 7z + z2 = 7 The z term is 7z. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7z + 12.25 + z2 = 7 + 12.25 Reorder the terms: 12.25 + 7z + z2 = 7 + 12.25 Combine like terms: 7 + 12.25 = 19.25 12.25 + 7z + z2 = 19.25 Factor a perfect square on the left side: (z + 3.5)(z + 3.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (z + 3.5) equal to 4.387482194 and -4.387482194.Subproblem 1
z + 3.5 = 4.387482194 Simplifying z + 3.5 = 4.387482194 Reorder the terms: 3.5 + z = 4.387482194 Solving 3.5 + z = 4.387482194 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + z = 4.387482194 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + z = 4.387482194 + -3.5 z = 4.387482194 + -3.5 Combine like terms: 4.387482194 + -3.5 = 0.887482194 z = 0.887482194 Simplifying z = 0.887482194Subproblem 2
z + 3.5 = -4.387482194 Simplifying z + 3.5 = -4.387482194 Reorder the terms: 3.5 + z = -4.387482194 Solving 3.5 + z = -4.387482194 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + z = -4.387482194 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + z = -4.387482194 + -3.5 z = -4.387482194 + -3.5 Combine like terms: -4.387482194 + -3.5 = -7.887482194 z = -7.887482194 Simplifying z = -7.887482194Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.887482194, -7.887482194}
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