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Simplifying 24x2 + 8x + 2 = 5 + -6x Reorder the terms: 2 + 8x + 24x2 = 5 + -6x Solving 2 + 8x + 24x2 = 5 + -6x Solving for variable 'x'. Reorder the terms: 2 + -5 + 8x + 6x + 24x2 = 5 + -6x + -5 + 6x Combine like terms: 2 + -5 = -3 -3 + 8x + 6x + 24x2 = 5 + -6x + -5 + 6x Combine like terms: 8x + 6x = 14x -3 + 14x + 24x2 = 5 + -6x + -5 + 6x Reorder the terms: -3 + 14x + 24x2 = 5 + -5 + -6x + 6x Combine like terms: 5 + -5 = 0 -3 + 14x + 24x2 = 0 + -6x + 6x -3 + 14x + 24x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -3 + 14x + 24x2 = 0 Factor a trinomial. (-3 + -4x)(1 + -6x) = 0Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(1 + -6x)' equal to zero and attempt to solve: Simplifying 1 + -6x = 0 Solving 1 + -6x = 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 + -6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x = 0 + -1 -6x = 0 + -1 Combine like terms: 0 + -1 = -1 -6x = -1 Divide each side by '-6'. x = 0.1666666667 Simplifying x = 0.1666666667Solution
x = {-0.75, 0.1666666667}
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