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Simplifying 18z + 45 = z2 Reorder the terms: 45 + 18z = z2 Solving 45 + 18z = z2 Solving for variable 'z'. Combine like terms: z2 + -1z2 = 0 45 + 18z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + -18z + z2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -18z + 45 + z2 = 0 + 45 Reorder the terms: -45 + 45 + -18z + z2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -18z + z2 = 0 + 45 -18z + z2 = 0 + 45 Combine like terms: 0 + 45 = 45 -18z + z2 = 45 The z term is -18z. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18z + 81 + z2 = 45 + 81 Reorder the terms: 81 + -18z + z2 = 45 + 81 Combine like terms: 45 + 81 = 126 81 + -18z + z2 = 126 Factor a perfect square on the left side: (z + -9)(z + -9) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (z + -9) equal to 11.22497216 and -11.22497216.Subproblem 1
z + -9 = 11.22497216 Simplifying z + -9 = 11.22497216 Reorder the terms: -9 + z = 11.22497216 Solving -9 + z = 11.22497216 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + z = 11.22497216 + 9 z = 11.22497216 + 9 Combine like terms: 11.22497216 + 9 = 20.22497216 z = 20.22497216 Simplifying z = 20.22497216Subproblem 2
z + -9 = -11.22497216 Simplifying z + -9 = -11.22497216 Reorder the terms: -9 + z = -11.22497216 Solving -9 + z = -11.22497216 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = -11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + z = -11.22497216 + 9 z = -11.22497216 + 9 Combine like terms: -11.22497216 + 9 = -2.22497216 z = -2.22497216 Simplifying z = -2.22497216Solution
The solution to the problem is based on the solutions from the subproblems. z = {20.22497216, -2.22497216}
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