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Simplifying z2 + 12z + 36z = 4 Reorder the terms: 12z + 36z + z2 = 4 Combine like terms: 12z + 36z = 48z 48z + z2 = 4 Solving 48z + z2 = 4 Solving for variable 'z'. Reorder the terms: -4 + 48z + z2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 48z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 48z + 4 + z2 = 0 + 4 Reorder the terms: -4 + 4 + 48z + z2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 48z + z2 = 0 + 4 48z + z2 = 0 + 4 Combine like terms: 0 + 4 = 4 48z + z2 = 4 The z term is 48z. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48z + 576 + z2 = 4 + 576 Reorder the terms: 576 + 48z + z2 = 4 + 576 Combine like terms: 4 + 576 = 580 576 + 48z + z2 = 580 Factor a perfect square on the left side: (z + 24)(z + 24) = 580 Calculate the square root of the right side: 24.083189158 Break this problem into two subproblems by setting (z + 24) equal to 24.083189158 and -24.083189158.Subproblem 1
z + 24 = 24.083189158 Simplifying z + 24 = 24.083189158 Reorder the terms: 24 + z = 24.083189158 Solving 24 + z = 24.083189158 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + z = 24.083189158 + -24 Combine like terms: 24 + -24 = 0 0 + z = 24.083189158 + -24 z = 24.083189158 + -24 Combine like terms: 24.083189158 + -24 = 0.083189158 z = 0.083189158 Simplifying z = 0.083189158Subproblem 2
z + 24 = -24.083189158 Simplifying z + 24 = -24.083189158 Reorder the terms: 24 + z = -24.083189158 Solving 24 + z = -24.083189158 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + z = -24.083189158 + -24 Combine like terms: 24 + -24 = 0 0 + z = -24.083189158 + -24 z = -24.083189158 + -24 Combine like terms: -24.083189158 + -24 = -48.083189158 z = -48.083189158 Simplifying z = -48.083189158Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.083189158, -48.083189158}
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