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Simplifying 4x4 = 65x2 + -196 Reorder the terms: 4x4 = -196 + 65x2 Solving 4x4 = -196 + 65x2 Solving for variable 'x'. Reorder the terms: 196 + -65x2 + 4x4 = -196 + 65x2 + 196 + -65x2 Reorder the terms: 196 + -65x2 + 4x4 = -196 + 196 + 65x2 + -65x2 Combine like terms: -196 + 196 = 0 196 + -65x2 + 4x4 = 0 + 65x2 + -65x2 196 + -65x2 + 4x4 = 65x2 + -65x2 Combine like terms: 65x2 + -65x2 = 0 196 + -65x2 + 4x4 = 0 Factor a trinomial. (4 + -1x2)(49 + -4x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(49 + -4x2) = 0 Factor a difference between two squares. ((7 + 2x)(7 + -2x))(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 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 4
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {-2, 2, -3.5, 3.5}
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