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Simplifying 48 = z(z + 6) Reorder the terms: 48 = z(6 + z) 48 = (6 * z + z * z) 48 = (6z + z2) Solving 48 = 6z + z2 Solving for variable 'z'. Reorder the terms: 48 + -6z + -1z2 = 6z + -6z + z2 + -1z2 Combine like terms: 6z + -6z = 0 48 + -6z + -1z2 = 0 + z2 + -1z2 48 + -6z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 48 + -6z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 6z + z2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 6z + 48 + z2 = 0 + 48 Reorder the terms: -48 + 48 + 6z + z2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 6z + z2 = 0 + 48 6z + z2 = 0 + 48 Combine like terms: 0 + 48 = 48 6z + z2 = 48 The z term is 6z. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6z + 9 + z2 = 48 + 9 Reorder the terms: 9 + 6z + z2 = 48 + 9 Combine like terms: 48 + 9 = 57 9 + 6z + z2 = 57 Factor a perfect square on the left side: (z + 3)(z + 3) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (z + 3) equal to 7.549834435 and -7.549834435.Subproblem 1
z + 3 = 7.549834435 Simplifying z + 3 = 7.549834435 Reorder the terms: 3 + z = 7.549834435 Solving 3 + z = 7.549834435 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + z = 7.549834435 + -3 z = 7.549834435 + -3 Combine like terms: 7.549834435 + -3 = 4.549834435 z = 4.549834435 Simplifying z = 4.549834435Subproblem 2
z + 3 = -7.549834435 Simplifying z + 3 = -7.549834435 Reorder the terms: 3 + z = -7.549834435 Solving 3 + z = -7.549834435 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = -7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + z = -7.549834435 + -3 z = -7.549834435 + -3 Combine like terms: -7.549834435 + -3 = -10.549834435 z = -10.549834435 Simplifying z = -10.549834435Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.549834435, -10.549834435}
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