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Simplifying x2(x2 + -81) + -49(x2 + -81) = 0 Reorder the terms: x2(-81 + x2) + -49(x2 + -81) = 0 (-81 * x2 + x2 * x2) + -49(x2 + -81) = 0 (-81x2 + x4) + -49(x2 + -81) = 0 Reorder the terms: -81x2 + x4 + -49(-81 + x2) = 0 -81x2 + x4 + (-81 * -49 + x2 * -49) = 0 -81x2 + x4 + (3969 + -49x2) = 0 Reorder the terms: 3969 + -81x2 + -49x2 + x4 = 0 Combine like terms: -81x2 + -49x2 = -130x2 3969 + -130x2 + x4 = 0 Solving 3969 + -130x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (49 + -1x2)(81 + -1x2) = 0 Factor a difference between two squares. ((7 + x)(7 + -1x))(81 + -1x2) = 0 Factor a difference between two squares. ((9 + x)(9 + -1x))(7 + x)(7 + -1x) = 0Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 3
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 4
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-7, 7, -9, 9}
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