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Simplifying 144x2 + 24x + 1 = x2 + 4x + 4 Reorder the terms: 1 + 24x + 144x2 = x2 + 4x + 4 Reorder the terms: 1 + 24x + 144x2 = 4 + 4x + x2 Solving 1 + 24x + 144x2 = 4 + 4x + x2 Solving for variable 'x'. Reorder the terms: 1 + -4 + 24x + -4x + 144x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2 Combine like terms: 1 + -4 = -3 -3 + 24x + -4x + 144x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2 Combine like terms: 24x + -4x = 20x -3 + 20x + 144x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2 Combine like terms: 144x2 + -1x2 = 143x2 -3 + 20x + 143x2 = 4 + 4x + x2 + -4 + -4x + -1x2 Reorder the terms: -3 + 20x + 143x2 = 4 + -4 + 4x + -4x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -3 + 20x + 143x2 = 0 + 4x + -4x + x2 + -1x2 -3 + 20x + 143x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -3 + 20x + 143x2 = 0 + x2 + -1x2 -3 + 20x + 143x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + 20x + 143x2 = 0 Factor a trinomial. (-3 + -13x)(1 + -11x) = 0Subproblem 1
Set the factor '(-3 + -13x)' equal to zero and attempt to solve: Simplifying -3 + -13x = 0 Solving -3 + -13x = 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 + -13x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -13x = 0 + 3 -13x = 0 + 3 Combine like terms: 0 + 3 = 3 -13x = 3 Divide each side by '-13'. x = -0.2307692308 Simplifying x = -0.2307692308Subproblem 2
Set the factor '(1 + -11x)' equal to zero and attempt to solve: Simplifying 1 + -11x = 0 Solving 1 + -11x = 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 + -11x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -11x = 0 + -1 -11x = 0 + -1 Combine like terms: 0 + -1 = -1 -11x = -1 Divide each side by '-11'. x = 0.09090909091 Simplifying x = 0.09090909091Solution
x = {-0.2307692308, 0.09090909091}
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