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Simplifying 16x4 = 65x2 + -49 Reorder the terms: 16x4 = -49 + 65x2 Solving 16x4 = -49 + 65x2 Solving for variable 'x'. Reorder the terms: 49 + -65x2 + 16x4 = -49 + 65x2 + 49 + -65x2 Reorder the terms: 49 + -65x2 + 16x4 = -49 + 49 + 65x2 + -65x2 Combine like terms: -49 + 49 = 0 49 + -65x2 + 16x4 = 0 + 65x2 + -65x2 49 + -65x2 + 16x4 = 65x2 + -65x2 Combine like terms: 65x2 + -65x2 = 0 49 + -65x2 + 16x4 = 0 Factor a trinomial. (1 + -1x2)(49 + -16x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(49 + -16x2) = 0 Factor a difference between two squares. ((7 + 4x)(7 + -4x))(1 + x)(1 + -1x) = 0Subproblem 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 '(7 + 4x)' equal to zero and attempt to solve: Simplifying 7 + 4x = 0 Solving 7 + 4x = 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 + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x = 0 + -7 4x = 0 + -7 Combine like terms: 0 + -7 = -7 4x = -7 Divide each side by '4'. x = -1.75 Simplifying x = -1.75Subproblem 4
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Solution
x = {-1, 1, -1.75, 1.75}
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