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Simplifying 9z2 + 36z + 25 = 0 Reorder the terms: 25 + 36z + 9z2 = 0 Solving 25 + 36z + 9z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.777777778 + 4z + z2 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + 4z + -2.777777778 + z2 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + 4z + z2 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + 4z + z2 = 0 + -2.777777778 4z + z2 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 4z + z2 = -2.777777778 The z term is 4z. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z + 4 + z2 = -2.777777778 + 4 Reorder the terms: 4 + 4z + z2 = -2.777777778 + 4 Combine like terms: -2.777777778 + 4 = 1.222222222 4 + 4z + z2 = 1.222222222 Factor a perfect square on the left side: (z + 2)(z + 2) = 1.222222222 Calculate the square root of the right side: 1.105541597 Break this problem into two subproblems by setting (z + 2) equal to 1.105541597 and -1.105541597.Subproblem 1
z + 2 = 1.105541597 Simplifying z + 2 = 1.105541597 Reorder the terms: 2 + z = 1.105541597 Solving 2 + z = 1.105541597 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 1.105541597 + -2 Combine like terms: 2 + -2 = 0 0 + z = 1.105541597 + -2 z = 1.105541597 + -2 Combine like terms: 1.105541597 + -2 = -0.894458403 z = -0.894458403 Simplifying z = -0.894458403Subproblem 2
z + 2 = -1.105541597 Simplifying z + 2 = -1.105541597 Reorder the terms: 2 + z = -1.105541597 Solving 2 + z = -1.105541597 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = -1.105541597 + -2 Combine like terms: 2 + -2 = 0 0 + z = -1.105541597 + -2 z = -1.105541597 + -2 Combine like terms: -1.105541597 + -2 = -3.105541597 z = -3.105541597 Simplifying z = -3.105541597Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.894458403, -3.105541597}
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