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Simplifying -1z2 + -14z + 43 = 0 Reorder the terms: 43 + -14z + -1z2 = 0 Solving 43 + -14z + -1z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -43 + 14z + z2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + 14z + 43 + z2 = 0 + 43 Reorder the terms: -43 + 43 + 14z + z2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 14z + z2 = 0 + 43 14z + z2 = 0 + 43 Combine like terms: 0 + 43 = 43 14z + z2 = 43 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 = 43 + 49 Reorder the terms: 49 + 14z + z2 = 43 + 49 Combine like terms: 43 + 49 = 92 49 + 14z + z2 = 92 Factor a perfect square on the left side: (z + 7)(z + 7) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (z + 7) equal to 9.591663047 and -9.591663047.Subproblem 1
z + 7 = 9.591663047 Simplifying z + 7 = 9.591663047 Reorder the terms: 7 + z = 9.591663047 Solving 7 + z = 9.591663047 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 = 9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + z = 9.591663047 + -7 z = 9.591663047 + -7 Combine like terms: 9.591663047 + -7 = 2.591663047 z = 2.591663047 Simplifying z = 2.591663047Subproblem 2
z + 7 = -9.591663047 Simplifying z + 7 = -9.591663047 Reorder the terms: 7 + z = -9.591663047 Solving 7 + z = -9.591663047 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 = -9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + z = -9.591663047 + -7 z = -9.591663047 + -7 Combine like terms: -9.591663047 + -7 = -16.591663047 z = -16.591663047 Simplifying z = -16.591663047Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.591663047, -16.591663047}
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