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Simplifying -150 + 10z + z2 = 0 Solving -150 + 10z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 10z + 150 + z2 = 0 + 150 Reorder the terms: -150 + 150 + 10z + z2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 10z + z2 = 0 + 150 10z + z2 = 0 + 150 Combine like terms: 0 + 150 = 150 10z + z2 = 150 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 = 150 + 25 Reorder the terms: 25 + 10z + z2 = 150 + 25 Combine like terms: 150 + 25 = 175 25 + 10z + z2 = 175 Factor a perfect square on the left side: (z + 5)(z + 5) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (z + 5) equal to 13.228756555 and -13.228756555.Subproblem 1
z + 5 = 13.228756555 Simplifying z + 5 = 13.228756555 Reorder the terms: 5 + z = 13.228756555 Solving 5 + z = 13.228756555 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 = 13.228756555 + -5 Combine like terms: 5 + -5 = 0 0 + z = 13.228756555 + -5 z = 13.228756555 + -5 Combine like terms: 13.228756555 + -5 = 8.228756555 z = 8.228756555 Simplifying z = 8.228756555Subproblem 2
z + 5 = -13.228756555 Simplifying z + 5 = -13.228756555 Reorder the terms: 5 + z = -13.228756555 Solving 5 + z = -13.228756555 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 = -13.228756555 + -5 Combine like terms: 5 + -5 = 0 0 + z = -13.228756555 + -5 z = -13.228756555 + -5 Combine like terms: -13.228756555 + -5 = -18.228756555 z = -18.228756555 Simplifying z = -18.228756555Solution
The solution to the problem is based on the solutions from the subproblems. z = {8.228756555, -18.228756555}
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