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Simplifying 3z2 + -87z = -21 Reorder the terms: -87z + 3z2 = -21 Solving -87z + 3z2 = -21 Solving for variable 'z'. Reorder the terms: 21 + -87z + 3z2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -87z + 3z2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -29z + z2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -29z + z2)' equal to zero and attempt to solve: Simplifying 7 + -29z + z2 = 0 Solving 7 + -29z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -29z + -7 + z2 = 0 + -7 Reorder the terms: 7 + -7 + -29z + z2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -29z + z2 = 0 + -7 -29z + z2 = 0 + -7 Combine like terms: 0 + -7 = -7 -29z + z2 = -7 The z term is -29z. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29z + 210.25 + z2 = -7 + 210.25 Reorder the terms: 210.25 + -29z + z2 = -7 + 210.25 Combine like terms: -7 + 210.25 = 203.25 210.25 + -29z + z2 = 203.25 Factor a perfect square on the left side: (z + -14.5)(z + -14.5) = 203.25 Calculate the square root of the right side: 14.256577429 Break this problem into two subproblems by setting (z + -14.5) equal to 14.256577429 and -14.256577429.Subproblem 1
z + -14.5 = 14.256577429 Simplifying z + -14.5 = 14.256577429 Reorder the terms: -14.5 + z = 14.256577429 Solving -14.5 + z = 14.256577429 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + z = 14.256577429 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + z = 14.256577429 + 14.5 z = 14.256577429 + 14.5 Combine like terms: 14.256577429 + 14.5 = 28.756577429 z = 28.756577429 Simplifying z = 28.756577429Subproblem 2
z + -14.5 = -14.256577429 Simplifying z + -14.5 = -14.256577429 Reorder the terms: -14.5 + z = -14.256577429 Solving -14.5 + z = -14.256577429 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + z = -14.256577429 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + z = -14.256577429 + 14.5 z = -14.256577429 + 14.5 Combine like terms: -14.256577429 + 14.5 = 0.243422571 z = 0.243422571 Simplifying z = 0.243422571Solution
The solution to the problem is based on the solutions from the subproblems. z = {28.756577429, 0.243422571}Solution
z = {28.756577429, 0.243422571}
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