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Simplifying z2 + -1064z + 5972 = 0 Reorder the terms: 5972 + -1064z + z2 = 0 Solving 5972 + -1064z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-5972' to each side of the equation. 5972 + -1064z + -5972 + z2 = 0 + -5972 Reorder the terms: 5972 + -5972 + -1064z + z2 = 0 + -5972 Combine like terms: 5972 + -5972 = 0 0 + -1064z + z2 = 0 + -5972 -1064z + z2 = 0 + -5972 Combine like terms: 0 + -5972 = -5972 -1064z + z2 = -5972 The z term is -1064z. Take half its coefficient (-532). Square it (283024) and add it to both sides. Add '283024' to each side of the equation. -1064z + 283024 + z2 = -5972 + 283024 Reorder the terms: 283024 + -1064z + z2 = -5972 + 283024 Combine like terms: -5972 + 283024 = 277052 283024 + -1064z + z2 = 277052 Factor a perfect square on the left side: (z + -532)(z + -532) = 277052 Calculate the square root of the right side: 526.3572931 Break this problem into two subproblems by setting (z + -532) equal to 526.3572931 and -526.3572931.Subproblem 1
z + -532 = 526.3572931 Simplifying z + -532 = 526.3572931 Reorder the terms: -532 + z = 526.3572931 Solving -532 + z = 526.3572931 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '532' to each side of the equation. -532 + 532 + z = 526.3572931 + 532 Combine like terms: -532 + 532 = 0 0 + z = 526.3572931 + 532 z = 526.3572931 + 532 Combine like terms: 526.3572931 + 532 = 1058.3572931 z = 1058.3572931 Simplifying z = 1058.3572931Subproblem 2
z + -532 = -526.3572931 Simplifying z + -532 = -526.3572931 Reorder the terms: -532 + z = -526.3572931 Solving -532 + z = -526.3572931 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '532' to each side of the equation. -532 + 532 + z = -526.3572931 + 532 Combine like terms: -532 + 532 = 0 0 + z = -526.3572931 + 532 z = -526.3572931 + 532 Combine like terms: -526.3572931 + 532 = 5.6427069 z = 5.6427069 Simplifying z = 5.6427069Solution
The solution to the problem is based on the solutions from the subproblems. z = {1058.3572931, 5.6427069}
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