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Simplifying x2(x2 + -16) + -49(x2 + -16) = 0 Reorder the terms: x2(-16 + x2) + -49(x2 + -16) = 0 (-16 * x2 + x2 * x2) + -49(x2 + -16) = 0 (-16x2 + x4) + -49(x2 + -16) = 0 Reorder the terms: -16x2 + x4 + -49(-16 + x2) = 0 -16x2 + x4 + (-16 * -49 + x2 * -49) = 0 -16x2 + x4 + (784 + -49x2) = 0 Reorder the terms: 784 + -16x2 + -49x2 + x4 = 0 Combine like terms: -16x2 + -49x2 = -65x2 784 + -65x2 + x4 = 0 Solving 784 + -65x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (16 + -1x2)(49 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -1x))(49 + -1x2) = 0 Factor a difference between two squares. ((7 + x)(7 + -1x))(4 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 3
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 4
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 = 7Solution
x = {-4, 4, -7, 7}
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