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Simplifying (x2 + -25)(x2 + -49) = 0 Reorder the terms: (-25 + x2)(x2 + -49) = 0 Reorder the terms: (-25 + x2)(-49 + x2) = 0 Multiply (-25 + x2) * (-49 + x2) (-25(-49 + x2) + x2(-49 + x2)) = 0 ((-49 * -25 + x2 * -25) + x2(-49 + x2)) = 0 ((1225 + -25x2) + x2(-49 + x2)) = 0 (1225 + -25x2 + (-49 * x2 + x2 * x2)) = 0 (1225 + -25x2 + (-49x2 + x4)) = 0 Combine like terms: -25x2 + -49x2 = -74x2 (1225 + -74x2 + x4) = 0 Solving 1225 + -74x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (25 + -1x2)(49 + -1x2) = 0 Factor a difference between two squares. ((5 + x)(5 + -1x))(49 + -1x2) = 0 Factor a difference between two squares. ((7 + x)(7 + -1x))(5 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 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 = {-5, 5, -7, 7}
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