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Simplifying z2 + 98z + -64 = 0 Reorder the terms: -64 + 98z + z2 = 0 Solving -64 + 98z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 98z + 64 + z2 = 0 + 64 Reorder the terms: -64 + 64 + 98z + z2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 98z + z2 = 0 + 64 98z + z2 = 0 + 64 Combine like terms: 0 + 64 = 64 98z + z2 = 64 The z term is 98z. Take half its coefficient (49). Square it (2401) and add it to both sides. Add '2401' to each side of the equation. 98z + 2401 + z2 = 64 + 2401 Reorder the terms: 2401 + 98z + z2 = 64 + 2401 Combine like terms: 64 + 2401 = 2465 2401 + 98z + z2 = 2465 Factor a perfect square on the left side: (z + 49)(z + 49) = 2465 Calculate the square root of the right side: 49.648766349 Break this problem into two subproblems by setting (z + 49) equal to 49.648766349 and -49.648766349.Subproblem 1
z + 49 = 49.648766349 Simplifying z + 49 = 49.648766349 Reorder the terms: 49 + z = 49.648766349 Solving 49 + z = 49.648766349 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + z = 49.648766349 + -49 Combine like terms: 49 + -49 = 0 0 + z = 49.648766349 + -49 z = 49.648766349 + -49 Combine like terms: 49.648766349 + -49 = 0.648766349 z = 0.648766349 Simplifying z = 0.648766349Subproblem 2
z + 49 = -49.648766349 Simplifying z + 49 = -49.648766349 Reorder the terms: 49 + z = -49.648766349 Solving 49 + z = -49.648766349 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-49' to each side of the equation. 49 + -49 + z = -49.648766349 + -49 Combine like terms: 49 + -49 = 0 0 + z = -49.648766349 + -49 z = -49.648766349 + -49 Combine like terms: -49.648766349 + -49 = -98.648766349 z = -98.648766349 Simplifying z = -98.648766349Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.648766349, -98.648766349}
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