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Simplifying 4x4 + -11x2 + 7 = 0 Reorder the terms: 7 + -11x2 + 4x4 = 0 Solving 7 + -11x2 + 4x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(7 + -4x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(7 + -4x2) = 0Subproblem 1
Set the factor '(7 + -4x2)' equal to zero and attempt to solve: Simplifying 7 + -4x2 = 0 Solving 7 + -4x2 = 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 + -4x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x2 = 0 + -7 -4x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -4x2 = -7 Divide each side by '-4'. x2 = 1.75 Simplifying x2 = 1.75 Take the square root of each side: x = {-1.322875656, 1.322875656}Subproblem 2
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 3
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 = 1Solution
x = {-1.322875656, 1.322875656, -1, 1}
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