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Simplifying -1z2 + z + 13 = 0 Reorder the terms: 13 + z + -1z2 = 0 Solving 13 + z + -1z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + -1z + z2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -1z + 13 + z2 = 0 + 13 Reorder the terms: -13 + 13 + -1z + z2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1z + z2 = 0 + 13 -1z + z2 = 0 + 13 Combine like terms: 0 + 13 = 13 -1z + z2 = 13 The z term is z. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1z + 0.25 + z2 = 13 + 0.25 Reorder the terms: 0.25 + -1z + z2 = 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + -1z + z2 = 13.25 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (z + 0.5) equal to 3.640054945 and -3.640054945.Subproblem 1
z + 0.5 = 3.640054945 Simplifying z + 0.5 = 3.640054945 Reorder the terms: 0.5 + z = 3.640054945 Solving 0.5 + z = 3.640054945 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 3.640054945 + -0.5 z = 3.640054945 + -0.5 Combine like terms: 3.640054945 + -0.5 = 3.140054945 z = 3.140054945 Simplifying z = 3.140054945Subproblem 2
z + 0.5 = -3.640054945 Simplifying z + 0.5 = -3.640054945 Reorder the terms: 0.5 + z = -3.640054945 Solving 0.5 + z = -3.640054945 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = -3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -3.640054945 + -0.5 z = -3.640054945 + -0.5 Combine like terms: -3.640054945 + -0.5 = -4.140054945 z = -4.140054945 Simplifying z = -4.140054945Solution
The solution to the problem is based on the solutions from the subproblems. z = {3.140054945, -4.140054945}
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