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Simplifying z2 + -12z = -13 Reorder the terms: -12z + z2 = -13 Solving -12z + z2 = -13 Solving for variable 'z'. Reorder the terms: 13 + -12z + z2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -12z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -12z + -13 + z2 = 0 + -13 Reorder the terms: 13 + -13 + -12z + z2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -12z + z2 = 0 + -13 -12z + z2 = 0 + -13 Combine like terms: 0 + -13 = -13 -12z + z2 = -13 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 = -13 + 36 Reorder the terms: 36 + -12z + z2 = -13 + 36 Combine like terms: -13 + 36 = 23 36 + -12z + z2 = 23 Factor a perfect square on the left side: (z + -6)(z + -6) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (z + -6) equal to 4.795831523 and -4.795831523.Subproblem 1
z + -6 = 4.795831523 Simplifying z + -6 = 4.795831523 Reorder the terms: -6 + z = 4.795831523 Solving -6 + z = 4.795831523 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 = 4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + z = 4.795831523 + 6 z = 4.795831523 + 6 Combine like terms: 4.795831523 + 6 = 10.795831523 z = 10.795831523 Simplifying z = 10.795831523Subproblem 2
z + -6 = -4.795831523 Simplifying z + -6 = -4.795831523 Reorder the terms: -6 + z = -4.795831523 Solving -6 + z = -4.795831523 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 = -4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + z = -4.795831523 + 6 z = -4.795831523 + 6 Combine like terms: -4.795831523 + 6 = 1.204168477 z = 1.204168477 Simplifying z = 1.204168477Solution
The solution to the problem is based on the solutions from the subproblems. z = {10.795831523, 1.204168477}
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