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Simplifying 12x3 = 27x2 + 15x Reorder the terms: 12x3 = 15x + 27x2 Solving 12x3 = 15x + 27x2 Solving for variable 'x'. Reorder the terms: -15x + -27x2 + 12x3 = 15x + 27x2 + -15x + -27x2 Reorder the terms: -15x + -27x2 + 12x3 = 15x + -15x + 27x2 + -27x2 Combine like terms: 15x + -15x = 0 -15x + -27x2 + 12x3 = 0 + 27x2 + -27x2 -15x + -27x2 + 12x3 = 27x2 + -27x2 Combine like terms: 27x2 + -27x2 = 0 -15x + -27x2 + 12x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-5 + -9x + 4x2) = 0 Ignore the factor 3.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 '(-5 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + -9x + 4x2 = 0 Solving -5 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -2.25x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.25x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.25x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.25x + x2 = 0 + 1.25 -2.25x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.25x + x2 = 1.25 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 1.25 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 1.25 + 1.265625 Combine like terms: 1.25 + 1.265625 = 2.515625 1.265625 + -2.25x + x2 = 2.515625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + -1.125) equal to 1.586072193 and -1.586072193.Subproblem 1
x + -1.125 = 1.586072193 Simplifying x + -1.125 = 1.586072193 Reorder the terms: -1.125 + x = 1.586072193 Solving -1.125 + x = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.586072193 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.586072193 + 1.125 x = 1.586072193 + 1.125 Combine like terms: 1.586072193 + 1.125 = 2.711072193 x = 2.711072193 Simplifying x = 2.711072193Subproblem 2
x + -1.125 = -1.586072193 Simplifying x + -1.125 = -1.586072193 Reorder the terms: -1.125 + x = -1.586072193 Solving -1.125 + x = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.586072193 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.586072193 + 1.125 x = -1.586072193 + 1.125 Combine like terms: -1.586072193 + 1.125 = -0.461072193 x = -0.461072193 Simplifying x = -0.461072193Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.711072193, -0.461072193}Solution
x = {0, 2.711072193, -0.461072193}
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