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Simplifying (z2 + -49)(z2 + -64) = 0 Reorder the terms: (-49 + z2)(z2 + -64) = 0 Reorder the terms: (-49 + z2)(-64 + z2) = 0 Multiply (-49 + z2) * (-64 + z2) (-49(-64 + z2) + z2(-64 + z2)) = 0 ((-64 * -49 + z2 * -49) + z2(-64 + z2)) = 0 ((3136 + -49z2) + z2(-64 + z2)) = 0 (3136 + -49z2 + (-64 * z2 + z2 * z2)) = 0 (3136 + -49z2 + (-64z2 + z4)) = 0 Combine like terms: -49z2 + -64z2 = -113z2 (3136 + -113z2 + z4) = 0 Solving 3136 + -113z2 + z4 = 0 Solving for variable 'z'. Factor a trinomial. (49 + -1z2)(64 + -1z2) = 0 Factor a difference between two squares. ((7 + z)(7 + -1z))(64 + -1z2) = 0 Factor a difference between two squares. ((8 + z)(8 + -1z))(7 + z)(7 + -1z) = 0Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 0 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 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 2
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Subproblem 3
Set the factor '(8 + z)' equal to zero and attempt to solve: Simplifying 8 + z = 0 Solving 8 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z = 0 + -8 z = 0 + -8 Combine like terms: 0 + -8 = -8 z = -8 Simplifying z = -8Subproblem 4
Set the factor '(8 + -1z)' equal to zero and attempt to solve: Simplifying 8 + -1z = 0 Solving 8 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1z = 0 + -8 -1z = 0 + -8 Combine like terms: 0 + -8 = -8 -1z = -8 Divide each side by '-1'. z = 8 Simplifying z = 8Solution
z = {-7, 7, -8, 8}
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