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Simplifying -885 + 12z + 3z2 = 0 Solving -885 + 12z + 3z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3'. 3(-295 + 4z + z2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-295 + 4z + z2)' equal to zero and attempt to solve: Simplifying -295 + 4z + z2 = 0 Solving -295 + 4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '295' to each side of the equation. -295 + 4z + 295 + z2 = 0 + 295 Reorder the terms: -295 + 295 + 4z + z2 = 0 + 295 Combine like terms: -295 + 295 = 0 0 + 4z + z2 = 0 + 295 4z + z2 = 0 + 295 Combine like terms: 0 + 295 = 295 4z + z2 = 295 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 = 295 + 4 Reorder the terms: 4 + 4z + z2 = 295 + 4 Combine like terms: 295 + 4 = 299 4 + 4z + z2 = 299 Factor a perfect square on the left side: (z + 2)(z + 2) = 299 Calculate the square root of the right side: 17.291616466 Break this problem into two subproblems by setting (z + 2) equal to 17.291616466 and -17.291616466.Subproblem 1
z + 2 = 17.291616466 Simplifying z + 2 = 17.291616466 Reorder the terms: 2 + z = 17.291616466 Solving 2 + z = 17.291616466 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 = 17.291616466 + -2 Combine like terms: 2 + -2 = 0 0 + z = 17.291616466 + -2 z = 17.291616466 + -2 Combine like terms: 17.291616466 + -2 = 15.291616466 z = 15.291616466 Simplifying z = 15.291616466Subproblem 2
z + 2 = -17.291616466 Simplifying z + 2 = -17.291616466 Reorder the terms: 2 + z = -17.291616466 Solving 2 + z = -17.291616466 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 = -17.291616466 + -2 Combine like terms: 2 + -2 = 0 0 + z = -17.291616466 + -2 z = -17.291616466 + -2 Combine like terms: -17.291616466 + -2 = -19.291616466 z = -19.291616466 Simplifying z = -19.291616466Solution
The solution to the problem is based on the solutions from the subproblems. z = {15.291616466, -19.291616466}Solution
z = {15.291616466, -19.291616466}
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