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Simplifying 3z2 + 12z + -49 = 0 Reorder the terms: -49 + 12z + 3z2 = 0 Solving -49 + 12z + 3z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.33333333 + 4z + z2 = 0 Move the constant term to the right: Add '16.33333333' to each side of the equation. -16.33333333 + 4z + 16.33333333 + z2 = 0 + 16.33333333 Reorder the terms: -16.33333333 + 16.33333333 + 4z + z2 = 0 + 16.33333333 Combine like terms: -16.33333333 + 16.33333333 = 0.00000000 0.00000000 + 4z + z2 = 0 + 16.33333333 4z + z2 = 0 + 16.33333333 Combine like terms: 0 + 16.33333333 = 16.33333333 4z + z2 = 16.33333333 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 = 16.33333333 + 4 Reorder the terms: 4 + 4z + z2 = 16.33333333 + 4 Combine like terms: 16.33333333 + 4 = 20.33333333 4 + 4z + z2 = 20.33333333 Factor a perfect square on the left side: (z + 2)(z + 2) = 20.33333333 Calculate the square root of the right side: 4.509249752 Break this problem into two subproblems by setting (z + 2) equal to 4.509249752 and -4.509249752.Subproblem 1
z + 2 = 4.509249752 Simplifying z + 2 = 4.509249752 Reorder the terms: 2 + z = 4.509249752 Solving 2 + z = 4.509249752 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 = 4.509249752 + -2 Combine like terms: 2 + -2 = 0 0 + z = 4.509249752 + -2 z = 4.509249752 + -2 Combine like terms: 4.509249752 + -2 = 2.509249752 z = 2.509249752 Simplifying z = 2.509249752Subproblem 2
z + 2 = -4.509249752 Simplifying z + 2 = -4.509249752 Reorder the terms: 2 + z = -4.509249752 Solving 2 + z = -4.509249752 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 = -4.509249752 + -2 Combine like terms: 2 + -2 = 0 0 + z = -4.509249752 + -2 z = -4.509249752 + -2 Combine like terms: -4.509249752 + -2 = -6.509249752 z = -6.509249752 Simplifying z = -6.509249752Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.509249752, -6.509249752}
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