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Simplifying 24x3 + -9x2 + -18x = 3x Reorder the terms: -18x + -9x2 + 24x3 = 3x Solving -18x + -9x2 + 24x3 = 3x Solving for variable 'x'. Reorder the terms: -18x + -3x + -9x2 + 24x3 = 3x + -3x Combine like terms: -18x + -3x = -21x -21x + -9x2 + 24x3 = 3x + -3x Combine like terms: 3x + -3x = 0 -21x + -9x2 + 24x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-7 + -3x + 8x2) = 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 '(-7 + -3x + 8x2)' equal to zero and attempt to solve: Simplifying -7 + -3x + 8x2 = 0 Solving -7 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -0.375x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -0.375x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -0.375x + x2 = 0 + 0.875 -0.375x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -0.375x + x2 = 0.875 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.875 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.875 + 0.03515625 Combine like terms: 0.875 + 0.03515625 = 0.91015625 0.03515625 + -0.375x + x2 = 0.91015625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.91015625 Calculate the square root of the right side: 0.954021095 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.954021095 and -0.954021095.Subproblem 1
x + -0.1875 = 0.954021095 Simplifying x + -0.1875 = 0.954021095 Reorder the terms: -0.1875 + x = 0.954021095 Solving -0.1875 + x = 0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.954021095 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.954021095 + 0.1875 x = 0.954021095 + 0.1875 Combine like terms: 0.954021095 + 0.1875 = 1.141521095 x = 1.141521095 Simplifying x = 1.141521095Subproblem 2
x + -0.1875 = -0.954021095 Simplifying x + -0.1875 = -0.954021095 Reorder the terms: -0.1875 + x = -0.954021095 Solving -0.1875 + x = -0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.954021095 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.954021095 + 0.1875 x = -0.954021095 + 0.1875 Combine like terms: -0.954021095 + 0.1875 = -0.766521095 x = -0.766521095 Simplifying x = -0.766521095Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.141521095, -0.766521095}Solution
x = {0, 1.141521095, -0.766521095}
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