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Simplifying z2 + 14z + -48 = 0 Reorder the terms: -48 + 14z + z2 = 0 Solving -48 + 14z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 14z + 48 + z2 = 0 + 48 Reorder the terms: -48 + 48 + 14z + z2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 14z + z2 = 0 + 48 14z + z2 = 0 + 48 Combine like terms: 0 + 48 = 48 14z + z2 = 48 The z term is 14z. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14z + 49 + z2 = 48 + 49 Reorder the terms: 49 + 14z + z2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + 14z + z2 = 97 Factor a perfect square on the left side: (z + 7)(z + 7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (z + 7) equal to 9.848857802 and -9.848857802.Subproblem 1
z + 7 = 9.848857802 Simplifying z + 7 = 9.848857802 Reorder the terms: 7 + z = 9.848857802 Solving 7 + z = 9.848857802 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + z = 9.848857802 + -7 z = 9.848857802 + -7 Combine like terms: 9.848857802 + -7 = 2.848857802 z = 2.848857802 Simplifying z = 2.848857802Subproblem 2
z + 7 = -9.848857802 Simplifying z + 7 = -9.848857802 Reorder the terms: 7 + z = -9.848857802 Solving 7 + z = -9.848857802 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = -9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + z = -9.848857802 + -7 z = -9.848857802 + -7 Combine like terms: -9.848857802 + -7 = -16.848857802 z = -16.848857802 Simplifying z = -16.848857802Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.848857802, -16.848857802}
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