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Simplifying z2 + -2z + -48 = (2 + -8)(z + 0) Reorder the terms: -48 + -2z + z2 = (2 + -8)(z + 0) Combine like terms: 2 + -8 = -6 -48 + -2z + z2 = (-6)(z + 0) Reorder the terms: -48 + -2z + z2 = -6(0 + z) Remove the zero: -48 + -2z + z2 = -6(z) Solving -48 + -2z + z2 = -6z Solving for variable 'z'. Reorder the terms: -48 + -2z + 6z + z2 = -6z + 6z Combine like terms: -2z + 6z = 4z -48 + 4z + z2 = -6z + 6z Combine like terms: -6z + 6z = 0 -48 + 4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 4z + 48 + z2 = 0 + 48 Reorder the terms: -48 + 48 + 4z + z2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 4z + z2 = 0 + 48 4z + z2 = 0 + 48 Combine like terms: 0 + 48 = 48 4z + z2 = 48 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 = 48 + 4 Reorder the terms: 4 + 4z + z2 = 48 + 4 Combine like terms: 48 + 4 = 52 4 + 4z + z2 = 52 Factor a perfect square on the left side: (z + 2)(z + 2) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (z + 2) equal to 7.211102551 and -7.211102551.Subproblem 1
z + 2 = 7.211102551 Simplifying z + 2 = 7.211102551 Reorder the terms: 2 + z = 7.211102551 Solving 2 + z = 7.211102551 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 = 7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + z = 7.211102551 + -2 z = 7.211102551 + -2 Combine like terms: 7.211102551 + -2 = 5.211102551 z = 5.211102551 Simplifying z = 5.211102551Subproblem 2
z + 2 = -7.211102551 Simplifying z + 2 = -7.211102551 Reorder the terms: 2 + z = -7.211102551 Solving 2 + z = -7.211102551 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 = -7.211102551 + -2 Combine like terms: 2 + -2 = 0 0 + z = -7.211102551 + -2 z = -7.211102551 + -2 Combine like terms: -7.211102551 + -2 = -9.211102551 z = -9.211102551 Simplifying z = -9.211102551Solution
The solution to the problem is based on the solutions from the subproblems. z = {5.211102551, -9.211102551}
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