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Simplifying z2 + -2z + -10 = 87 Reorder the terms: -10 + -2z + z2 = 87 Solving -10 + -2z + z2 = 87 Solving for variable 'z'. Reorder the terms: -10 + -87 + -2z + z2 = 87 + -87 Combine like terms: -10 + -87 = -97 -97 + -2z + z2 = 87 + -87 Combine like terms: 87 + -87 = 0 -97 + -2z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + -2z + 97 + z2 = 0 + 97 Reorder the terms: -97 + 97 + -2z + z2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + -2z + z2 = 0 + 97 -2z + z2 = 0 + 97 Combine like terms: 0 + 97 = 97 -2z + z2 = 97 The z term is -2z. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2z + 1 + z2 = 97 + 1 Reorder the terms: 1 + -2z + z2 = 97 + 1 Combine like terms: 97 + 1 = 98 1 + -2z + z2 = 98 Factor a perfect square on the left side: (z + -1)(z + -1) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (z + -1) equal to 9.899494937 and -9.899494937.Subproblem 1
z + -1 = 9.899494937 Simplifying z + -1 = 9.899494937 Reorder the terms: -1 + z = 9.899494937 Solving -1 + z = 9.899494937 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + z = 9.899494937 + 1 Combine like terms: -1 + 1 = 0 0 + z = 9.899494937 + 1 z = 9.899494937 + 1 Combine like terms: 9.899494937 + 1 = 10.899494937 z = 10.899494937 Simplifying z = 10.899494937Subproblem 2
z + -1 = -9.899494937 Simplifying z + -1 = -9.899494937 Reorder the terms: -1 + z = -9.899494937 Solving -1 + z = -9.899494937 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + z = -9.899494937 + 1 Combine like terms: -1 + 1 = 0 0 + z = -9.899494937 + 1 z = -9.899494937 + 1 Combine like terms: -9.899494937 + 1 = -8.899494937 z = -8.899494937 Simplifying z = -8.899494937Solution
The solution to the problem is based on the solutions from the subproblems. z = {10.899494937, -8.899494937}
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