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Simplifying z2 + -7z + -30 = z Reorder the terms: -30 + -7z + z2 = z Solving -30 + -7z + z2 = z Solving for variable 'z'. Reorder the terms: -30 + -7z + -1z + z2 = z + -1z Combine like terms: -7z + -1z = -8z -30 + -8z + z2 = z + -1z Combine like terms: z + -1z = 0 -30 + -8z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -8z + 30 + z2 = 0 + 30 Reorder the terms: -30 + 30 + -8z + z2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -8z + z2 = 0 + 30 -8z + z2 = 0 + 30 Combine like terms: 0 + 30 = 30 -8z + z2 = 30 The z term is -8z. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8z + 16 + z2 = 30 + 16 Reorder the terms: 16 + -8z + z2 = 30 + 16 Combine like terms: 30 + 16 = 46 16 + -8z + z2 = 46 Factor a perfect square on the left side: (z + -4)(z + -4) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (z + -4) equal to 6.782329983 and -6.782329983.Subproblem 1
z + -4 = 6.782329983 Simplifying z + -4 = 6.782329983 Reorder the terms: -4 + z = 6.782329983 Solving -4 + z = 6.782329983 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 6.782329983 + 4 Combine like terms: -4 + 4 = 0 0 + z = 6.782329983 + 4 z = 6.782329983 + 4 Combine like terms: 6.782329983 + 4 = 10.782329983 z = 10.782329983 Simplifying z = 10.782329983Subproblem 2
z + -4 = -6.782329983 Simplifying z + -4 = -6.782329983 Reorder the terms: -4 + z = -6.782329983 Solving -4 + z = -6.782329983 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = -6.782329983 + 4 Combine like terms: -4 + 4 = 0 0 + z = -6.782329983 + 4 z = -6.782329983 + 4 Combine like terms: -6.782329983 + 4 = -2.782329983 z = -2.782329983 Simplifying z = -2.782329983Solution
The solution to the problem is based on the solutions from the subproblems. z = {10.782329983, -2.782329983}
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