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Simplifying z2 = 10z + -20 Reorder the terms: z2 = -20 + 10z Solving z2 = -20 + 10z Solving for variable 'z'. Reorder the terms: 20 + -10z + z2 = -20 + 10z + 20 + -10z Reorder the terms: 20 + -10z + z2 = -20 + 20 + 10z + -10z Combine like terms: -20 + 20 = 0 20 + -10z + z2 = 0 + 10z + -10z 20 + -10z + z2 = 10z + -10z Combine like terms: 10z + -10z = 0 20 + -10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -10z + -20 + z2 = 0 + -20 Reorder the terms: 20 + -20 + -10z + z2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -10z + z2 = 0 + -20 -10z + z2 = 0 + -20 Combine like terms: 0 + -20 = -20 -10z + z2 = -20 The z term is -10z. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10z + 25 + z2 = -20 + 25 Reorder the terms: 25 + -10z + z2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + -10z + z2 = 5 Factor a perfect square on the left side: (z + -5)(z + -5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (z + -5) equal to 2.236067978 and -2.236067978.Subproblem 1
z + -5 = 2.236067978 Simplifying z + -5 = 2.236067978 Reorder the terms: -5 + z = 2.236067978 Solving -5 + z = 2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + z = 2.236067978 + 5 z = 2.236067978 + 5 Combine like terms: 2.236067978 + 5 = 7.236067978 z = 7.236067978 Simplifying z = 7.236067978Subproblem 2
z + -5 = -2.236067978 Simplifying z + -5 = -2.236067978 Reorder the terms: -5 + z = -2.236067978 Solving -5 + z = -2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + z = -2.236067978 + 5 z = -2.236067978 + 5 Combine like terms: -2.236067978 + 5 = 2.763932022 z = 2.763932022 Simplifying z = 2.763932022Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.236067978, 2.763932022}
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