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Simplifying 4X4 + 36 = 40X2 Reorder the terms: 36 + 4X4 = 40X2 Solving 36 + 4X4 = 40X2 Solving for variable 'X'. Reorder the terms: 36 + -40X2 + 4X4 = 40X2 + -40X2 Combine like terms: 40X2 + -40X2 = 0 36 + -40X2 + 4X4 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -10X2 + X4) = 0 Factor a trinomial. 4((1 + -1X2)(9 + -1X2)) = 0 Factor a difference between two squares. 4(((1 + X)(1 + -1X))(9 + -1X2)) = 0 Factor a difference between two squares. 4(((3 + X)(3 + -1X))(1 + X)(1 + -1X)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + X)' equal to zero and attempt to solve: Simplifying 1 + X = 0 Solving 1 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + X = 0 + -1 X = 0 + -1 Combine like terms: 0 + -1 = -1 X = -1 Simplifying X = -1Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve: Simplifying 1 + -1X = 0 Solving 1 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1X = 0 + -1 -1X = 0 + -1 Combine like terms: 0 + -1 = -1 -1X = -1 Divide each side by '-1'. X = 1 Simplifying X = 1Subproblem 3
Set the factor '(3 + X)' equal to zero and attempt to solve: Simplifying 3 + X = 0 Solving 3 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = 0 + -3 Combine like terms: 3 + -3 = 0 0 + X = 0 + -3 X = 0 + -3 Combine like terms: 0 + -3 = -3 X = -3 Simplifying X = -3Subproblem 4
Set the factor '(3 + -1X)' equal to zero and attempt to solve: Simplifying 3 + -1X = 0 Solving 3 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1X = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1X = 0 + -3 -1X = 0 + -3 Combine like terms: 0 + -3 = -3 -1X = -3 Divide each side by '-1'. X = 3 Simplifying X = 3Solution
X = {-1, 1, -3, 3}
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