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Simplifying z2 + -4z = 30 Reorder the terms: -4z + z2 = 30 Solving -4z + z2 = 30 Solving for variable 'z'. Reorder the terms: -30 + -4z + z2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -4z + 30 + z2 = 0 + 30 Reorder the terms: -30 + 30 + -4z + z2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -4z + z2 = 0 + 30 -4z + z2 = 0 + 30 Combine like terms: 0 + 30 = 30 -4z + z2 = 30 The z term is -4z. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4z + 4 + z2 = 30 + 4 Reorder the terms: 4 + -4z + z2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + -4z + z2 = 34 Factor a perfect square on the left side: (z + -2)(z + -2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (z + -2) equal to 5.830951895 and -5.830951895.Subproblem 1
z + -2 = 5.830951895 Simplifying z + -2 = 5.830951895 Reorder the terms: -2 + z = 5.830951895 Solving -2 + z = 5.830951895 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + z = 5.830951895 + 2 z = 5.830951895 + 2 Combine like terms: 5.830951895 + 2 = 7.830951895 z = 7.830951895 Simplifying z = 7.830951895Subproblem 2
z + -2 = -5.830951895 Simplifying z + -2 = -5.830951895 Reorder the terms: -2 + z = -5.830951895 Solving -2 + z = -5.830951895 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = -5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + z = -5.830951895 + 2 z = -5.830951895 + 2 Combine like terms: -5.830951895 + 2 = -3.830951895 z = -3.830951895 Simplifying z = -3.830951895Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.830951895, -3.830951895}
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