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Simplifying z2 + -12z = 9 Reorder the terms: -12z + z2 = 9 Solving -12z + z2 = 9 Solving for variable 'z'. Reorder the terms: -9 + -12z + z2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -12z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -12z + 9 + z2 = 0 + 9 Reorder the terms: -9 + 9 + -12z + z2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -12z + z2 = 0 + 9 -12z + z2 = 0 + 9 Combine like terms: 0 + 9 = 9 -12z + z2 = 9 The z term is -12z. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12z + 36 + z2 = 9 + 36 Reorder the terms: 36 + -12z + z2 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + -12z + z2 = 45 Factor a perfect square on the left side: (z + -6)(z + -6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (z + -6) equal to 6.708203933 and -6.708203933.Subproblem 1
z + -6 = 6.708203933 Simplifying z + -6 = 6.708203933 Reorder the terms: -6 + z = 6.708203933 Solving -6 + z = 6.708203933 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = 6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + z = 6.708203933 + 6 z = 6.708203933 + 6 Combine like terms: 6.708203933 + 6 = 12.708203933 z = 12.708203933 Simplifying z = 12.708203933Subproblem 2
z + -6 = -6.708203933 Simplifying z + -6 = -6.708203933 Reorder the terms: -6 + z = -6.708203933 Solving -6 + z = -6.708203933 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = -6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + z = -6.708203933 + 6 z = -6.708203933 + 6 Combine like terms: -6.708203933 + 6 = -0.708203933 z = -0.708203933 Simplifying z = -0.708203933Solution
The solution to the problem is based on the solutions from the subproblems. z = {12.708203933, -0.708203933}
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