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Simplifying z2 + -13z = 12 Reorder the terms: -13z + z2 = 12 Solving -13z + z2 = 12 Solving for variable 'z'. Reorder the terms: -12 + -13z + z2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -13z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -13z + 12 + z2 = 0 + 12 Reorder the terms: -12 + 12 + -13z + z2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -13z + z2 = 0 + 12 -13z + z2 = 0 + 12 Combine like terms: 0 + 12 = 12 -13z + z2 = 12 The z term is -13z. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13z + 42.25 + z2 = 12 + 42.25 Reorder the terms: 42.25 + -13z + z2 = 12 + 42.25 Combine like terms: 12 + 42.25 = 54.25 42.25 + -13z + z2 = 54.25 Factor a perfect square on the left side: (z + -6.5)(z + -6.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (z + -6.5) equal to 7.365459931 and -7.365459931.Subproblem 1
z + -6.5 = 7.365459931 Simplifying z + -6.5 = 7.365459931 Reorder the terms: -6.5 + z = 7.365459931 Solving -6.5 + z = 7.365459931 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + z = 7.365459931 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + z = 7.365459931 + 6.5 z = 7.365459931 + 6.5 Combine like terms: 7.365459931 + 6.5 = 13.865459931 z = 13.865459931 Simplifying z = 13.865459931Subproblem 2
z + -6.5 = -7.365459931 Simplifying z + -6.5 = -7.365459931 Reorder the terms: -6.5 + z = -7.365459931 Solving -6.5 + z = -7.365459931 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + z = -7.365459931 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + z = -7.365459931 + 6.5 z = -7.365459931 + 6.5 Combine like terms: -7.365459931 + 6.5 = -0.865459931 z = -0.865459931 Simplifying z = -0.865459931Solution
The solution to the problem is based on the solutions from the subproblems. z = {13.865459931, -0.865459931}
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