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Simplifying 12x(x2 + -24x + 1) = 0 Reorder the terms: 12x(1 + -24x + x2) = 0 (1 * 12x + -24x * 12x + x2 * 12x) = 0 (12x + -288x2 + 12x3) = 0 Solving 12x + -288x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12x'. 12x(1 + -24x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -24x + x2)' equal to zero and attempt to solve: Simplifying 1 + -24x + x2 = 0 Solving 1 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -24x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -24x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -24x + x2 = 0 + -1 -24x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -24x + x2 = -1 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -1 + 144 Reorder the terms: 144 + -24x + x2 = -1 + 144 Combine like terms: -1 + 144 = 143 144 + -24x + x2 = 143 Factor a perfect square on the left side: (x + -12)(x + -12) = 143 Calculate the square root of the right side: 11.958260743 Break this problem into two subproblems by setting (x + -12) equal to 11.958260743 and -11.958260743.Subproblem 1
x + -12 = 11.958260743 Simplifying x + -12 = 11.958260743 Reorder the terms: -12 + x = 11.958260743 Solving -12 + x = 11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.958260743 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.958260743 + 12 x = 11.958260743 + 12 Combine like terms: 11.958260743 + 12 = 23.958260743 x = 23.958260743 Simplifying x = 23.958260743Subproblem 2
x + -12 = -11.958260743 Simplifying x + -12 = -11.958260743 Reorder the terms: -12 + x = -11.958260743 Solving -12 + x = -11.958260743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.958260743 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.958260743 + 12 x = -11.958260743 + 12 Combine like terms: -11.958260743 + 12 = 0.041739257 x = 0.041739257 Simplifying x = 0.041739257Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.958260743, 0.041739257}Solution
x = {0, 23.958260743, 0.041739257}
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