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Simplifying z2 + -9z + 15 = 0 Reorder the terms: 15 + -9z + z2 = 0 Solving 15 + -9z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -9z + -15 + z2 = 0 + -15 Reorder the terms: 15 + -15 + -9z + z2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -9z + z2 = 0 + -15 -9z + z2 = 0 + -15 Combine like terms: 0 + -15 = -15 -9z + z2 = -15 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 = -15 + 20.25 Reorder the terms: 20.25 + -9z + z2 = -15 + 20.25 Combine like terms: -15 + 20.25 = 5.25 20.25 + -9z + z2 = 5.25 Factor a perfect square on the left side: (z + -4.5)(z + -4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (z + -4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
z + -4.5 = 2.291287847 Simplifying z + -4.5 = 2.291287847 Reorder the terms: -4.5 + z = 2.291287847 Solving -4.5 + z = 2.291287847 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 = 2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + z = 2.291287847 + 4.5 z = 2.291287847 + 4.5 Combine like terms: 2.291287847 + 4.5 = 6.791287847 z = 6.791287847 Simplifying z = 6.791287847Subproblem 2
z + -4.5 = -2.291287847 Simplifying z + -4.5 = -2.291287847 Reorder the terms: -4.5 + z = -2.291287847 Solving -4.5 + z = -2.291287847 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 = -2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + z = -2.291287847 + 4.5 z = -2.291287847 + 4.5 Combine like terms: -2.291287847 + 4.5 = 2.208712153 z = 2.208712153 Simplifying z = 2.208712153Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.791287847, 2.208712153}
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