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Simplifying z2 + -10z = -7 Reorder the terms: -10z + z2 = -7 Solving -10z + z2 = -7 Solving for variable 'z'. Reorder the terms: 7 + -10z + z2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -10z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -10z + -7 + z2 = 0 + -7 Reorder the terms: 7 + -7 + -10z + z2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10z + z2 = 0 + -7 -10z + z2 = 0 + -7 Combine like terms: 0 + -7 = -7 -10z + z2 = -7 The z term is -10z. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10z + 25 + z2 = -7 + 25 Reorder the terms: 25 + -10z + z2 = -7 + 25 Combine like terms: -7 + 25 = 18 25 + -10z + z2 = 18 Factor a perfect square on the left side: (z + -5)(z + -5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (z + -5) equal to 4.242640687 and -4.242640687.Subproblem 1
z + -5 = 4.242640687 Simplifying z + -5 = 4.242640687 Reorder the terms: -5 + z = 4.242640687 Solving -5 + z = 4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + z = 4.242640687 + 5 z = 4.242640687 + 5 Combine like terms: 4.242640687 + 5 = 9.242640687 z = 9.242640687 Simplifying z = 9.242640687Subproblem 2
z + -5 = -4.242640687 Simplifying z + -5 = -4.242640687 Reorder the terms: -5 + z = -4.242640687 Solving -5 + z = -4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -4.242640687 + 5 Combine like terms: -5 + 5 = 0 0 + z = -4.242640687 + 5 z = -4.242640687 + 5 Combine like terms: -4.242640687 + 5 = 0.757359313 z = 0.757359313 Simplifying z = 0.757359313Solution
The solution to the problem is based on the solutions from the subproblems. z = {9.242640687, 0.757359313}
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