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Simplifying z2 + -14z = 40 Reorder the terms: -14z + z2 = 40 Solving -14z + z2 = 40 Solving for variable 'z'. Reorder the terms: -40 + -14z + z2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -14z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -14z + 40 + z2 = 0 + 40 Reorder the terms: -40 + 40 + -14z + z2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -14z + z2 = 0 + 40 -14z + z2 = 0 + 40 Combine like terms: 0 + 40 = 40 -14z + z2 = 40 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 = 40 + 49 Reorder the terms: 49 + -14z + z2 = 40 + 49 Combine like terms: 40 + 49 = 89 49 + -14z + z2 = 89 Factor a perfect square on the left side: (z + -7)(z + -7) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (z + -7) equal to 9.433981132 and -9.433981132.Subproblem 1
z + -7 = 9.433981132 Simplifying z + -7 = 9.433981132 Reorder the terms: -7 + z = 9.433981132 Solving -7 + z = 9.433981132 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 = 9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + z = 9.433981132 + 7 z = 9.433981132 + 7 Combine like terms: 9.433981132 + 7 = 16.433981132 z = 16.433981132 Simplifying z = 16.433981132Subproblem 2
z + -7 = -9.433981132 Simplifying z + -7 = -9.433981132 Reorder the terms: -7 + z = -9.433981132 Solving -7 + z = -9.433981132 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 = -9.433981132 + 7 Combine like terms: -7 + 7 = 0 0 + z = -9.433981132 + 7 z = -9.433981132 + 7 Combine like terms: -9.433981132 + 7 = -2.433981132 z = -2.433981132 Simplifying z = -2.433981132Solution
The solution to the problem is based on the solutions from the subproblems. z = {16.433981132, -2.433981132}
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