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Simplifying x2(x2 + -4) + -49(x2 + -4) = 0 Reorder the terms: x2(-4 + x2) + -49(x2 + -4) = 0 (-4 * x2 + x2 * x2) + -49(x2 + -4) = 0 (-4x2 + x4) + -49(x2 + -4) = 0 Reorder the terms: -4x2 + x4 + -49(-4 + x2) = 0 -4x2 + x4 + (-4 * -49 + x2 * -49) = 0 -4x2 + x4 + (196 + -49x2) = 0 Reorder the terms: 196 + -4x2 + -49x2 + x4 = 0 Combine like terms: -4x2 + -49x2 = -53x2 196 + -53x2 + x4 = 0 Solving 196 + -53x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (4 + -1x2)(49 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(49 + -1x2) = 0 Factor a difference between two squares. ((7 + x)(7 + -1x))(2 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {-2, 2, -7, 7}
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