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Simplifying -2z2 + -36z + -70 = 0 Reorder the terms: -70 + -36z + -2z2 = 0 Solving -70 + -36z + -2z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-2'. -2(35 + 18z + z2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(35 + 18z + z2)' equal to zero and attempt to solve: Simplifying 35 + 18z + z2 = 0 Solving 35 + 18z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 18z + -35 + z2 = 0 + -35 Reorder the terms: 35 + -35 + 18z + z2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 18z + z2 = 0 + -35 18z + z2 = 0 + -35 Combine like terms: 0 + -35 = -35 18z + z2 = -35 The z term is 18z. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18z + 81 + z2 = -35 + 81 Reorder the terms: 81 + 18z + z2 = -35 + 81 Combine like terms: -35 + 81 = 46 81 + 18z + z2 = 46 Factor a perfect square on the left side: (z + 9)(z + 9) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (z + 9) equal to 6.782329983 and -6.782329983.Subproblem 1
z + 9 = 6.782329983 Simplifying z + 9 = 6.782329983 Reorder the terms: 9 + z = 6.782329983 Solving 9 + z = 6.782329983 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 6.782329983 + -9 Combine like terms: 9 + -9 = 0 0 + z = 6.782329983 + -9 z = 6.782329983 + -9 Combine like terms: 6.782329983 + -9 = -2.217670017 z = -2.217670017 Simplifying z = -2.217670017Subproblem 2
z + 9 = -6.782329983 Simplifying z + 9 = -6.782329983 Reorder the terms: 9 + z = -6.782329983 Solving 9 + z = -6.782329983 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = -6.782329983 + -9 Combine like terms: 9 + -9 = 0 0 + z = -6.782329983 + -9 z = -6.782329983 + -9 Combine like terms: -6.782329983 + -9 = -15.782329983 z = -15.782329983 Simplifying z = -15.782329983Solution
The solution to the problem is based on the solutions from the subproblems. z = {-2.217670017, -15.782329983}Solution
z = {-2.217670017, -15.782329983}
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