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Simplifying z2 + 12z + -25 = 0 Reorder the terms: -25 + 12z + z2 = 0 Solving -25 + 12z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 12z + 25 + z2 = 0 + 25 Reorder the terms: -25 + 25 + 12z + z2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 12z + z2 = 0 + 25 12z + z2 = 0 + 25 Combine like terms: 0 + 25 = 25 12z + z2 = 25 The z term is 12z. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12z + 36 + z2 = 25 + 36 Reorder the terms: 36 + 12z + z2 = 25 + 36 Combine like terms: 25 + 36 = 61 36 + 12z + z2 = 61 Factor a perfect square on the left side: (z + 6)(z + 6) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (z + 6) equal to 7.810249676 and -7.810249676.Subproblem 1
z + 6 = 7.810249676 Simplifying z + 6 = 7.810249676 Reorder the terms: 6 + z = 7.810249676 Solving 6 + z = 7.810249676 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = 7.810249676 + -6 Combine like terms: 6 + -6 = 0 0 + z = 7.810249676 + -6 z = 7.810249676 + -6 Combine like terms: 7.810249676 + -6 = 1.810249676 z = 1.810249676 Simplifying z = 1.810249676Subproblem 2
z + 6 = -7.810249676 Simplifying z + 6 = -7.810249676 Reorder the terms: 6 + z = -7.810249676 Solving 6 + z = -7.810249676 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = -7.810249676 + -6 Combine like terms: 6 + -6 = 0 0 + z = -7.810249676 + -6 z = -7.810249676 + -6 Combine like terms: -7.810249676 + -6 = -13.810249676 z = -13.810249676 Simplifying z = -13.810249676Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.810249676, -13.810249676}
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