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Simplifying z2 + 9z = 7 Reorder the terms: 9z + z2 = 7 Solving 9z + z2 = 7 Solving for variable 'z'. Reorder the terms: -7 + 9z + z2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 9z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 9z + 7 + z2 = 0 + 7 Reorder the terms: -7 + 7 + 9z + z2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 9z + z2 = 0 + 7 9z + z2 = 0 + 7 Combine like terms: 0 + 7 = 7 9z + z2 = 7 The z term is 9z. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9z + 20.25 + z2 = 7 + 20.25 Reorder the terms: 20.25 + 9z + z2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + 9z + z2 = 27.25 Factor a perfect square on the left side: (z + 4.5)(z + 4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (z + 4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
z + 4.5 = 5.220153254 Simplifying z + 4.5 = 5.220153254 Reorder the terms: 4.5 + z = 5.220153254 Solving 4.5 + z = 5.220153254 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = 5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = 5.220153254 + -4.5 z = 5.220153254 + -4.5 Combine like terms: 5.220153254 + -4.5 = 0.720153254 z = 0.720153254 Simplifying z = 0.720153254Subproblem 2
z + 4.5 = -5.220153254 Simplifying z + 4.5 = -5.220153254 Reorder the terms: 4.5 + z = -5.220153254 Solving 4.5 + z = -5.220153254 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = -5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = -5.220153254 + -4.5 z = -5.220153254 + -4.5 Combine like terms: -5.220153254 + -4.5 = -9.720153254 z = -9.720153254 Simplifying z = -9.720153254Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.720153254, -9.720153254}
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