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Simplifying 2z2 + -9z + -9 = 0 Reorder the terms: -9 + -9z + 2z2 = 0 Solving -9 + -9z + 2z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -4.5z + z2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -4.5z + 4.5 + z2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -4.5z + z2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -4.5z + z2 = 0 + 4.5 -4.5z + z2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -4.5z + z2 = 4.5 The z term is -4.5z. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5z + 5.0625 + z2 = 4.5 + 5.0625 Reorder the terms: 5.0625 + -4.5z + z2 = 4.5 + 5.0625 Combine like terms: 4.5 + 5.0625 = 9.5625 5.0625 + -4.5z + z2 = 9.5625 Factor a perfect square on the left side: (z + -2.25)(z + -2.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (z + -2.25) equal to 3.092329219 and -3.092329219.Subproblem 1
z + -2.25 = 3.092329219 Simplifying z + -2.25 = 3.092329219 Reorder the terms: -2.25 + z = 3.092329219 Solving -2.25 + z = 3.092329219 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + z = 3.092329219 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + z = 3.092329219 + 2.25 z = 3.092329219 + 2.25 Combine like terms: 3.092329219 + 2.25 = 5.342329219 z = 5.342329219 Simplifying z = 5.342329219Subproblem 2
z + -2.25 = -3.092329219 Simplifying z + -2.25 = -3.092329219 Reorder the terms: -2.25 + z = -3.092329219 Solving -2.25 + z = -3.092329219 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + z = -3.092329219 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + z = -3.092329219 + 2.25 z = -3.092329219 + 2.25 Combine like terms: -3.092329219 + 2.25 = -0.842329219 z = -0.842329219 Simplifying z = -0.842329219Solution
The solution to the problem is based on the solutions from the subproblems. z = {5.342329219, -0.842329219}
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