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Simplifying z2 + -14z = 46 Reorder the terms: -14z + z2 = 46 Solving -14z + z2 = 46 Solving for variable 'z'. Reorder the terms: -46 + -14z + z2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -14z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -14z + 46 + z2 = 0 + 46 Reorder the terms: -46 + 46 + -14z + z2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -14z + z2 = 0 + 46 -14z + z2 = 0 + 46 Combine like terms: 0 + 46 = 46 -14z + z2 = 46 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 = 46 + 49 Reorder the terms: 49 + -14z + z2 = 46 + 49 Combine like terms: 46 + 49 = 95 49 + -14z + z2 = 95 Factor a perfect square on the left side: (z + -7)(z + -7) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (z + -7) equal to 9.746794345 and -9.746794345.Subproblem 1
z + -7 = 9.746794345 Simplifying z + -7 = 9.746794345 Reorder the terms: -7 + z = 9.746794345 Solving -7 + z = 9.746794345 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 = 9.746794345 + 7 Combine like terms: -7 + 7 = 0 0 + z = 9.746794345 + 7 z = 9.746794345 + 7 Combine like terms: 9.746794345 + 7 = 16.746794345 z = 16.746794345 Simplifying z = 16.746794345Subproblem 2
z + -7 = -9.746794345 Simplifying z + -7 = -9.746794345 Reorder the terms: -7 + z = -9.746794345 Solving -7 + z = -9.746794345 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 = -9.746794345 + 7 Combine like terms: -7 + 7 = 0 0 + z = -9.746794345 + 7 z = -9.746794345 + 7 Combine like terms: -9.746794345 + 7 = -2.746794345 z = -2.746794345 Simplifying z = -2.746794345Solution
The solution to the problem is based on the solutions from the subproblems. z = {16.746794345, -2.746794345}
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