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Simplifying z2 + -10z = -12 Reorder the terms: -10z + z2 = -12 Solving -10z + z2 = -12 Solving for variable 'z'. Reorder the terms: 12 + -10z + z2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -10z + -12 + z2 = 0 + -12 Reorder the terms: 12 + -12 + -10z + z2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -10z + z2 = 0 + -12 -10z + z2 = 0 + -12 Combine like terms: 0 + -12 = -12 -10z + z2 = -12 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 = -12 + 25 Reorder the terms: 25 + -10z + z2 = -12 + 25 Combine like terms: -12 + 25 = 13 25 + -10z + z2 = 13 Factor a perfect square on the left side: (z + -5)(z + -5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (z + -5) equal to 3.605551275 and -3.605551275.Subproblem 1
z + -5 = 3.605551275 Simplifying z + -5 = 3.605551275 Reorder the terms: -5 + z = 3.605551275 Solving -5 + z = 3.605551275 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 = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + z = 3.605551275 + 5 z = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 z = 8.605551275 Simplifying z = 8.605551275Subproblem 2
z + -5 = -3.605551275 Simplifying z + -5 = -3.605551275 Reorder the terms: -5 + z = -3.605551275 Solving -5 + z = -3.605551275 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 = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + z = -3.605551275 + 5 z = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 z = 1.394448725 Simplifying z = 1.394448725Solution
The solution to the problem is based on the solutions from the subproblems. z = {8.605551275, 1.394448725}
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