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Simplifying 72z + 18z2 + -18 = 0 Reorder the terms: -18 + 72z + 18z2 = 0 Solving -18 + 72z + 18z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '18'. 18(-1 + 4z + z2) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(-1 + 4z + z2)' equal to zero and attempt to solve: Simplifying -1 + 4z + z2 = 0 Solving -1 + 4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 4z + 1 + z2 = 0 + 1 Reorder the terms: -1 + 1 + 4z + z2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4z + z2 = 0 + 1 4z + z2 = 0 + 1 Combine like terms: 0 + 1 = 1 4z + z2 = 1 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 = 1 + 4 Reorder the terms: 4 + 4z + z2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4z + z2 = 5 Factor a perfect square on the left side: (z + 2)(z + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (z + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
z + 2 = 2.236067978 Simplifying z + 2 = 2.236067978 Reorder the terms: 2 + z = 2.236067978 Solving 2 + z = 2.236067978 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 = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + z = 2.236067978 + -2 z = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 z = 0.236067978 Simplifying z = 0.236067978Subproblem 2
z + 2 = -2.236067978 Simplifying z + 2 = -2.236067978 Reorder the terms: 2 + z = -2.236067978 Solving 2 + z = -2.236067978 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 = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + z = -2.236067978 + -2 z = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 z = -4.236067978 Simplifying z = -4.236067978Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.236067978, -4.236067978}Solution
z = {0.236067978, -4.236067978}
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